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Project Based Learning - Triangle Classification

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Project Based Learning - Triangle Classification

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Practice classifying triangles with a geometry art project your students will love! Read our February blog post to discover how your little learners can classify triangles by their angles or sides as they create a beautiful landscape picture featuring mountains. This math art project is a powerful teaching tool for helping kids understand triangle classifications. Read on to find out more!

Making Mountains: A Perfect Picture of Triangles

In this hands-on math activity, students will create a landscape picture featuring three triangle mountains. With the help of some graph paper, a pencil, and a ruler, students will draw their triangle mountains based on the three classifications of triangles by either angles or sides. For the first option, students will classify their triangle mountains as acute, obtuse, or right triangles. In the second option, students will classify the triangles as equilateral, scalene, or isosceles triangles. You can guide your students through one or both versions of the activity to help them grow in their knowledge of classifying triangles, but we recommend that you keep the classifications to two separate works of art to help avoid confusion and double-labeling. In addition to graph paper, a pencil, and a ruler, students will also need crayons, markers, colored pencils, construction paper, scissors, and glue.

Once you've gathered all the supplies, your students can make their triangle mountain landscapes in three easy steps.

Step One: Make Three Types of Triangles

First, students will use a pencil and a ruler to construct three different triangles from their graph paper. You can use this printable half-inch graph paper or this printable quarter-inch graph paper to get started. Children will draw an acute, obtuse, and right triangle. Or they will draw an equilateral, scalene, and isosceles triangle.

Your students' triangles do not need to be perfect, but they should demonstrate a thorough understanding of each type of triangle. For example, the obtuse triangle should have one obvious angle greater than 90 degrees and the right triangle should have its right angle labeled correctly. Encourage your students to label all their triangles on the lined side of the graph paper so they remember which one is which.

Step Two: Cut and Color the Triangle Mountains

Students will cut out the three triangles with a pair of scissors. They will then flip each triangle over to color the mountains on the plain, opposite side of the graph paper. Kids can decorate their triangle mountains with crayons, colored pencils, or markers.

Once students have added some colorful details to their triangular mountains, they should also label each one with its correct description by angle or side.

Step Three: Add Triangle Mountains to a Scenic Landscape

Students will finish their mountain artwork by adding their triangle mountains to a colorful landscape. Here are some fun ideas:

Create your own landscape by decorating a sheet of construction paper, computer paper, or scrapbook paper with crayons, colored pencils, or markers. Glue the triangle mountains onto the landscape background.

Find a scenic background to use by flipping through magazines, picking out a few postcards, or finding a natural background online.

Turn the project into a three-dimensional work of art by making a classic shoe-box diorama instead!

Your students can display their triangle mountain landscapes in a variety of ways-the sky's the limit! The most important thing to emphasize is your students' understanding of the different ways to classify triangles. Conclude the activity with a discussion of the different classifications of triangles.

Did you and your students try out this geometry art project to practice classifying triangles? How did it go? Leave us your feedback in the comment section below. Remember to tag @iknowit on social media so we can check out your scenic works of art!

To explore more fun, interactive math activities for your elementary students, browse hundreds of engaging math lessons available on iKnowIt.com.

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# data[].attributes.attachment_link.description
Practice classifying triangles with a geometry art project your students will love! Read our February blog post to discover how your little learners can classify triangles by their angles or sides as they create a beautiful landscape picture featuring mountains. This math art project is a powerful teaching tool for helping kids understand triangle classifications.

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Project Based Learning Assignment - Circles

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Project Based Learning Assignment - Circles

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Math + Arts | Circle Designs | PBS LearningMedia

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In this lesson, students explore circumference and diameter by creating an abstract design with circles.

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Lesson 3: Describe and Analyze Cross Sections of Circular Solids

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Lesson 3: Describe and Analyze Cross Sections of Circular Solids

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Lesson 2: Derive and Apply a Formula for the Area of a Circle

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Lesson 2: Derive and Apply a Formula for the Area of a Circle

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Lesson 1: How to Draw Circles and Other Figures

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Lesson 1: How to Draw Circles and Other Figures

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EdPuzzle: Drawing Polygons on a Coordinate Plane

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EdPuzzle: Drawing Polygons on a Coordinate Plane

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Easily create beautiful interactive video lessons for your students you can integrate right into your LMS. Track students' progress with hassle-free analytics as you flip your classroom!

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Easily create beautiful interactive video lessons for your students you can integrate right into your LMS. Track students' progress with hassle-free analytics as you flip your classroom!

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Easily create beautiful interactive video lessons for your students you can integrate right into your LMS. Track students' progress with hassle-free analytics as you flip your classroom!

# data[].attributes.attachment_link.description
Easily create beautiful interactive video lessons for your students you can integrate right into your LMS. Track students' progress with hassle-free analytics as you flip your classroom!

# data[].attributes.attachment_link.description
Easily create beautiful interactive video lessons for your students you can integrate right into your LMS. Track students' progress with hassle-free analytics as you flip your classroom!

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Easily create beautiful interactive video lessons for your students you can integrate right into your LMS. Track students' progress with hassle-free analytics as you flip your classroom!

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How to use Quizizz: Full tutorial for teachers!

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Lesson 1: Derive and Apply Forumulas for Circumference

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Lesson 1: Derive and Apply Forumulas for Circumference

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Beginner's Guide to Khan Academy for Teachers

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Game: Find the Missing Angle in a Triangle

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Game: Find the Missing Angle in a Triangle

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Can you work out the size of the angle marked with a letter in the given triangles?

This is level 1: find the marked angle in the triangle diagrams. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

This is Angles in a Triangle level 1. You can also try:
Level 2

© Transum Mathematics 1997-2023
Scan the QR code below to visit the online version of this activity.

https://Transum.org/go/?Num=143

Description of Levels

Close

It is assumed that the angles together on a straight line theorem is already known.

Level 1 - Find the marked angle in the triangle diagrams

Level 2 - More interesting problems about the angles in triangles

Angles at a point - Apply the properties of angles at a point, angles on a straight line and vertically opposite angles.

Angles with Parallel Lines - Understand and use the relationship between parallel lines and alternate and corresponding angles.

Polygon Angles - Practise the skills of finding interior and exterior angles of polygons to answer these questions.

Angles in Circles - Show that you understand the circle theorems with this self marking exercise.

More Angle Resources - including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Help

The diagrams are not drawn to scale but lines that look like straight lines can be taken as straight lines.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

The boxes made available to show working don't have to be used. It would be better to set out your working neatly in you exercise book but that may not always be practical.

+ The blue button allows you to add extra lines of working.

Please note that when the system marks your answers the working is not taken into consideration.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

Close

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Can you work out the size of the angle marked with a letter in the given triangles?

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Quiz: Finding Missing Angle of Triangles

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Quiz: Finding Missing Angle of Triangles

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Quizziz

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Finding missing angles | 79 plays | Quizizz

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Finding missing angles quiz for 5th grade students. Find other quizzes for Mathematics and more on Quizizz for free!

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7.Z.8

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IXL | Find missing angles in triangles | 7th grade math

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Improve your math knowledge with free questions in "Find missing angles in triangles" and thousands of other math skills.

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Triangle Inequality Based on Side Lengths

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Triangle Inequality Based on Side Lengths

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Z.3

Triangle inequality

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IXL | Triangle inequality | 7th grade math

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Improve your math knowledge with free questions in “Triangle inequality” and thousands of other math skills.

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7.Z.2

Classify triangles

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IXL | Classify triangles | 7th grade math

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Improve your math knowledge with free questions in “Classify triangles” and thousands of other math skills.

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Triangle Categorization Based on Angles and Side Lengths

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Triangle Categorization Based on Angles and Side Lengths

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4.G.A.2

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What I want to do in this video is talk about the two main ways that triangles are categorized. The first way is based on whether or not the triangle has equal sides, or at least a few equal sides. Then the other way is based on the measure of the angles of the triangle. So the first categorization right here, and all of these are based on whether or not the triangle has equal sides, is scalene. And a scalene triangle is a triangle where none of the sides are equal. So for example, if I have a triangle like this, where this side has length 3, this side has length 4, and this side has length 5, then this is going to be a scalene triangle. None of the sides have an equal length. Now an isosceles triangle is a triangle where at least two of the sides have equal lengths. So for example, this would be an isosceles triangle. Maybe this has length 3, this has length 3, and this has length 2. Notice, this side and this side are equal. So it meets the constraint of at least two of the three sides are have the same length. Now an equilateral triangle, you might imagine, and you'd be right, is a triangle where all three sides have the same length. So for example, this would be an equilateral triangle. And let's say that this has side 2, 2, and 2. Or if I have a triangle like this where it's 3, 3, and 3. Any triangle where all three sides have the same length is going to be equilateral. Now you might say, well Sal, didn't you just say that an isosceles triangle is a triangle has at least two sides being equal. Wouldn't an equilateral triangle be a special case of an isosceles triangle? And I would say yes, you're absolutely right. An equilateral triangle has all three sides equal, so it meets the constraints for an isosceles. So by that definition, all equilateral triangles are also isosceles triangles. But not all isosceles triangles are equilateral. So for example, this one right over here, this isosceles triangle, clearly not equilateral. All three sides are not the same. Only two are. But both of these equilateral triangles meet the constraint that at least two of the sides are equal. Now down here, we're going to classify based on angles. An acute triangle is a triangle where all of the angles are less than 90 degrees. So for example, a triangle like this-- maybe this is 60, let me draw a little bit bigger so I can draw the angle measures. That's a little bit less. I want to make it a little bit more obvious. So let's say a triangle like this. If this angle is 60 degrees, maybe this one right over here is 59 degrees. And then this angle right over here is 61 degrees. Notice they all add up to 180 degrees. This would be an acute triangle. Notice all of the angles are less than 90 degrees. A right triangle is a triangle that has one angle that is exactly 90 degrees. So for example, this right over here would be a right triangle. Maybe this angle or this angle is one that's 90 degrees. And the normal way that this is specified, people wouldn't just do the traditional angle measure and write 90 degrees here. They would draw the angle like this. They would put a little, the edge of a box-looking thing. And that tells you that this angle right over here is 90 degrees. And because this triangle has a 90 degree angle, and it could only have one 90 degree angle, this is a right triangle. So that is equal to 90 degrees. Now you could imagine an obtuse triangle, based on the idea that an obtuse angle is larger than 90 degrees, an obtuse triangle is a triangle that has one angle that is larger than 90 degrees. So let's say that you have a triangle that looks like this. Maybe this is 120 degrees. And then let's see, let me make sure that this would make sense. Maybe this is 25 degrees. Or maybe that is 35 degrees. And this is 25 degrees. Notice, they still add up to 180, or at least they should. 25 plus 35 is 60, plus 120, is 180 degrees. But the important point here is that we have an angle that is a larger, that is greater, than 90 degrees. Now, you might be asking yourself, hey Sal, can a triangle be multiple of these things. Can it be a right scalene triangle? Absolutely, you could have a right scalene triangle. In this situation right over here, actually a 3, 4, 5 triangle, a triangle that has lengths of 3, 4, and 5 actually is a right triangle. And this right over here would be a 90 degree angle. You could have an equilateral acute triangle. In fact, all equilateral triangles, because all of the angles are exactly 60 degrees, all equilateral triangles are actually acute. So there's multiple combinations that you could have between these situations and these situations right over here.

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Classifying triangles (video) | Khan Academy

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What I want to do in this video is talk about the two main ways that triangles are categorized. The first way is based on whether or not the triangle has equal sides, or at least a few equal sides. Then the other way is based on the measure of the angles of the triangle.

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7.G.A.2

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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7.G.A.2

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Triangle side length rules (practice) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Lesson 3: Draw and Construct Triangles Given Angle Measures

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Lesson 3: Draw and Construct Triangles Given Angle Measures

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Create triangles
See which combinations work and which do not

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Quiz: Drawing and Constructing Triangles

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Quiz: Drawing and Constructing Triangles

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Quizziz

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Constructing Triangles quiz for 6th grade students. Find other quizzes for Mathematics and more on Quizizz for free!

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You are using a very old browser, that is no longer supported by this site. We recommend that you upgrade to one of the following browsers:

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Triangle Inequality Based On Side Length

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Triangle Inequality Based On Side Length

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7.Z.3 Triangle inequality

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IXL | Triangle inequality | 7th grade math

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Improve your math knowledge with free questions in “Triangle inequality” and thousands of other math skills.

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7.G.A.2

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Can you build a triangle that is both a right triangle and an isosceles triangle? Created by Sal Khan.

Video transcript

They're asking us to draw a right triangle. So that means it has to have a 90-degree angle. But it's also an isosceles triangle, so that means it has to have at least two sides equal and has two sides of length 3. So those two sides that are going to be equal are going to be of length 3, and it's got to be a right triangle. So let's see if we can do that. So let's try to make this right over here the right angle. And let's make this side and this side have length 3, so 3 and then 3 right over there. Let me make sure I get that right angle right. OK, there you go. So it's a right angle. It's isosceles. At least two sides are equal. And the two sides have length 3. So it seems like we've met all of our constraints. Now they say, is there a unique triangle that satisfies this condition? So another way of rephrasing that, is this the only triangle that I could have drawn that meets these conditions? Well. I can't change this angle if I want to meet these conditions. I can't change these two lengths. And if you keep this angle constant and you keep these two lengths constant, then this point and this point are going to be there are no matter what. So this is the only side that can connect those two points. So this is the only triangle that meets those conditions. You can't have different side lengths, or you couldn't have different angles right over here and also meet those conditions. So is there a unique triangle that satisfies the given conditions? Yes, there's only one unique triangle.

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Construct a right isosceles triangle (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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4.G.A.2

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What I want to do in this video is talk about the two main ways that triangles are categorized. The first way is based on whether or not the triangle has equal sides, or at least a few equal sides. Then the other way is based on the measure of the angles of the triangle. So the first categorization right here, and all of these are based on whether or not the triangle has equal sides, is scalene. And a scalene triangle is a triangle where none of the sides are equal. So for example, if I have a triangle like this, where this side has length 3, this side has length 4, and this side has length 5, then this is going to be a scalene triangle. None of the sides have an equal length. Now an isosceles triangle is a triangle where at least two of the sides have equal lengths. So for example, this would be an isosceles triangle. Maybe this has length 3, this has length 3, and this has length 2. Notice, this side and this side are equal. So it meets the constraint of at least two of the three sides are have the same length. Now an equilateral triangle, you might imagine, and you'd be right, is a triangle where all three sides have the same length. So for example, this would be an equilateral triangle. And let's say that this has side 2, 2, and 2. Or if I have a triangle like this where it's 3, 3, and 3. Any triangle where all three sides have the same length is going to be equilateral. Now you might say, well Sal, didn't you just say that an isosceles triangle is a triangle has at least two sides being equal. Wouldn't an equilateral triangle be a special case of an isosceles triangle? And I would say yes, you're absolutely right. An equilateral triangle has all three sides equal, so it meets the constraints for an isosceles. So by that definition, all equilateral triangles are also isosceles triangles. But not all isosceles triangles are equilateral. So for example, this one right over here, this isosceles triangle, clearly not equilateral. All three sides are not the same. Only two are. But both of these equilateral triangles meet the constraint that at least two of the sides are equal. Now down here, we're going to classify based on angles. An acute triangle is a triangle where all of the angles are less than 90 degrees. So for example, a triangle like this-- maybe this is 60, let me draw a little bit bigger so I can draw the angle measures. That's a little bit less. I want to make it a little bit more obvious. So let's say a triangle like this. If this angle is 60 degrees, maybe this one right over here is 59 degrees. And then this angle right over here is 61 degrees. Notice they all add up to 180 degrees. This would be an acute triangle. Notice all of the angles are less than 90 degrees. A right triangle is a triangle that has one angle that is exactly 90 degrees. So for example, this right over here would be a right triangle. Maybe this angle or this angle is one that's 90 degrees. And the normal way that this is specified, people wouldn't just do the traditional angle measure and write 90 degrees here. They would draw the angle like this. They would put a little, the edge of a box-looking thing. And that tells you that this angle right over here is 90 degrees. And because this triangle has a 90 degree angle, and it could only have one 90 degree angle, this is a right triangle. So that is equal to 90 degrees. Now you could imagine an obtuse triangle, based on the idea that an obtuse angle is larger than 90 degrees, an obtuse triangle is a triangle that has one angle that is larger than 90 degrees. So let's say that you have a triangle that looks like this. Maybe this is 120 degrees. And then let's see, let me make sure that this would make sense. Maybe this is 25 degrees. Or maybe that is 35 degrees. And this is 25 degrees. Notice, they still add up to 180, or at least they should. 25 plus 35 is 60, plus 120, is 180 degrees. But the important point here is that we have an angle that is a larger, that is greater, than 90 degrees. Now, you might be asking yourself, hey Sal, can a triangle be multiple of these things. Can it be a right scalene triangle? Absolutely, you could have a right scalene triangle. In this situation right over here, actually a 3, 4, 5 triangle, a triangle that has lengths of 3, 4, and 5 actually is a right triangle. And this right over here would be a 90 degree angle. You could have an equilateral acute triangle. In fact, all equilateral triangles, because all of the angles are exactly 60 degrees, all equilateral triangles are actually acute. So there's multiple combinations that you could have between these situations and these situations right over here.

# data[].attributes.attachment_link.title
Classifying triangles (video) | Khan Academy

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What I want to do in this video is talk about the two main ways that triangles are categorized. The first way is based on whether or not the triangle has equal sides, or at least a few equal sides. Then the other way is based on the measure of the angles of the triangle.

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4.G.A.1

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Angle types (practice) | Plane figures | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Find The Area Of A Circle Online Crocodile Game

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Find The Area Of A Circle Online Crocodile Game - math game for 1st, 2nd, 3rd, 4th, 5th, 6th grades. Online basketball games free, Crocodile Game s For Kids Online, online crocodile video games.This game teaches students have to find the area of a circle using pie, radius squared. The value for pie is 3.14 while the radius is half the diameter.

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Quizziz

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Area of a Circle quiz for 7th grade students. Find other quizzes for Mathematics and more on Quizizz for free!

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Quizziz

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Identifying Parts of a Circle | 1.2K plays | Quizizz

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Identifying Parts of a Circle quiz for 9th grade students. Find other quizzes for Mathematics and more on Quizizz for free!

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Parts of a Circle - Grade 7 - Practice with Math Games

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Lesson 2: Draw and Construct Triangles Given Side Lengths

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Lesson 2: Draw and Construct Triangles Given Side Lengths

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5.QQ.7 Draw quadrilaterals

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IXL | Draw quadrilaterals | 5th grade math

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Improve your math knowledge with free questions in "Draw quadrilaterals" and thousands of other math skills.

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Drawing Polygons On a Coordinate Plane: 6.G.A.3

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Drawing Polygons On a Coordinate Plane: 6.G.A.3

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We're making a four-sided shape called a quadrilateral using line segments! We use four points on a graph: (0,9), (0,-7), (8,-7), and (8,0). We connect these points to form our quadrilateral. Isn't shape-making fun? Created by Sal Khan.

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Drawing a quadrilateral on the coordinate plane example (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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7.BB.6 Area of circle

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Improve your math knowledge with free questions in "Area of circles" and thousands of other math skills.

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# data[].attributes.attachment_link.title
Area of a circle (practice) | Geometry | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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7.Z.14

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IXL | Central angles of circles | 7th grade math

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Improve your math knowledge with free questions in "Central angles of circles" and thousands of other math skills.

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7.BB.5

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IXL | Circumference of circles | 7th grade math

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Improve your math knowledge with free questions in "Circumference of circles" and thousands of other math skills.

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Khan Academy Angles in a Circle: 4.MD.C.5.a, 4.MD.C.6

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Khan Academy Angles in a Circle: 4.MD.C.5.a, 4.MD.C.6

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Angles in circles (practice) | Khan Academy

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Khan Academy Circumference of a Circle: 7.G.B.4

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Khan Academy Circumference of a Circle: 7.G.B.4

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Circumference of a circle (practice) | Khan Academy

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7.Z.13

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IXL | Parts of a circle | 7th grade math

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Improve your math knowledge with free questions in “Parts of a circle” and thousands of other math skills.

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Khan Academy Circle Definitions: HSG.C.A.2

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Khan Academy Circle Definitions: HSG.C.A.2

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Let's start again with a point. Let's call that point point A. And what I'm curious about is all of the points on my screen right over here, that are exactly 2 centimeters away from A. So 2 centimeters on my screen is about that far. So clearly if I start at A and I go 2 centimeters in that direction, this point right over there, is 2 centimeters from A. If I call that point, point B, then I could say line segment AB is 2 centimeters. The length is 2 centimeters. Remember this would refer to the actual line segment. I could say this looks nice, but if I talk about its length, I would get rid of that line on top and I would just say AB is equal to 2. If I wanted to put units I could say 2 centimenters. But I'm not curious just about B, I want to think about all of the points, the set of all of the points that are exactly 2 centimeters away from A. So I could go 2 centimeters in the other direction, maybe get to point C right over here. So AC is also going to be equal to 2 centimeters, but I could go 2 centimeters in any direction. And so if I find the set of all of the points that are exactly 2 centimeters away from A, I will get a very familiar looking shape, like this, and I'm trying to draw it freehand. So I would get a shape that looks like this. Actually, let me draw it in. I don't want to make you think that it's only the points where there's white, it's all of these points right over here. I don't want to draw a dashed line over there, which maybe I should just, let me clear out all of these and I'll just draw it as a solid line. So this could look something like that. My best attempt. And this set of all of the points that are exactly 2 centimeters away from A, this is a circle, as I'm sure you are already familiar with. But that is the formal definition-- the set of all points that are a fixed distance, or that have a fixed distance, from A that are a given distance from A. If I said the set of all points that are 3 centimeters from A, it might look something like this. It might look something like that. That would give us another circle. I think you get the general idea. Now what I want to do in this video is introduce ourselves into some of the concepts and words that we use when dealing with circles. So let me get rid of that 3-centimeter circle. So first of all, let's think about this distance. This distance, or one of these line segments that join A, which we would call the center of the circle. So we'll call A the center of the circle, and it makes sense just from the way we use the word center in everyday life. What I want to do is think about what line segment AB is. AB connects the center and it connects a point on the circle itself. Remember, the circle itself is all of the points that are equal distance from the center. So AB, any line segment, I should say, that connects the center to a point on the circle, we would call a radius. And so the length of the radius, AB over here, is equal to 2 centimeters. And you're probably already familiar with the word radius, but I'm just being a little bit more formal. And what's interesting about geometry, at least when you start learning it at the high school level, is it's probably the first class where you're introduced into a slightly more formal mathematics, where we're a little bit more careful about giving our definitions and then building on those definitions to come up with interesting results and proving to ourselves that we definitely know what we think we know. And so that's why we're being a little bit more careful with our language over here. So AB is our radius, line segment AB, and so is line segment-- let me draw another point on here, let's say this is X-- so line segment AX is also a radius. Now you can also have other forms of lines and line segments that interact in interesting ways with the circle. So you could have a line that just intersects that circle at exactly one point. So let's call that point right over there, let's call that D. And let's say you have a line, and the only point on the circle-- the only point in the set of all of the points that are equal distant from A, the only point on that circle that is also on that line is point D. And we could call that line l. So sometimes you'll see lines specified by some of the points on them. So for example, if I had another point right over here called E, we could call this line line DE, or we could just put a little script letter here with an l and say this is line l. But this line that only has one point in common with our circle, we call this a tangent line. So line l is a tangent. It is tangent to the circle. So let me write it this way, line l is tangent-- you normally wouldn't write it in caps like this, I'm just doing that for emphasis-- is tangent to-- instead of writing the circle centered at A, you'll sometimes see this notation-- to the circle centered at A. So this tells us that this is the circle we're talking about. Because who knows, maybe we had another circle over here that is centered at M, another circle. So we have to specify it's not tangent to that one, it's tangent to this one. So this circle with a dot in the middle tells we're talking about a circle, and this is a circle centered at point A. I want to be very clear, point A is not on the circle, point A is the center of the circle. The points on the circle are the points equal distant from point A. Now, l is tangent, because it only intersects the circle in one point. You could just as easily imagine a line that intersects the circle at two points. So we could call, maybe this is F and this is G, you could call that line FG. So we could write it like this, line FG. And this line that intersects it at two points, we call this a secant of circle A. It is a secant line to this circle right over here, because it intersects it in two points. Now, if FG was just a segment, if it didn't keep on going forever, like lines like to do, if we only spoke about this line segment-- let me do this in a new color-- if we only spoke about this line segment between F and G, and not thinking about going on forever, then all of a sudden we have a line segment, which we would specify there. And we would call this a chord of the circle, a chord of circle A. It starts at a point on the circle, a point that is exactly in this case 2 centimeters away, and then it finishes at a point on the circle. So it connects two points on the circle. Now, you could have chords like this, and you can also have a chord, as you can imagine, a chord that actually goes through the center of the circle. So let's call this point, point H, and you have a straight line connecting F to H through A. So that's about as straight as I could draw it. So if you have a chord like that, that contains the actual center of the circle, of course it goes from one point of the circle to another point of the circle, and it goes through the center of the circle, we call that a diameter of A. And you've probably seen this in tons of problems before, when we were not talking about geometry as formally, but the diameter is made up of exactly two radiuses. We already know that a radius connects a point to the center. So you have one radius right over here that connects F and A, that's one radius, and then you have another radius connecting A and H, the center to a point on the circle. So the diameter is made up of these two radiuses, or radii I should call it, I think that's the plural for radius. And so the length of a diameter is going to be twice the length of a radius. So we could say the length of the diameter, so the length of FH-- and once again I don't put the line on top of it when I'm just talking about the length-- is going to be equal to FA, the length of segment FA, plus the length of segment AH. Now there's one last thing I want to talk about when we're dealing with circles, and that's the idea of an arc. So we also have the parts of the circle itself. So let me draw another circle over here. Let's center this circle right over here at B. And I'm going to find all of the points that are a given distance from B. So it has some radius, I'm not going to specify it right over here, and let me pick some random points on the circle. So let's call this J, let's call that K, let's call this S, let's call this T, let's call this U right over here. And I know it doesn't look that centered, let me try to center B a little bit better. Let me erase that. And if I put B a little bit closer to the center of the circle, so that's my best shot, so let's put B right over there. Now, one interesting thing is, what do you call the length of the circle that goes between two points? So what would you call-- let me get a good color here-- what would you call this? Well, you could imagine in everyday language we would call something that looks like that an arc, and we would also call that an arc in geometry. To specify this arc we would call this JK, the two endpoints of the arc, the two points on the circle that are the endpoints of the arc, and you use a little notation like that. So you put a little curve on top instead of a straight line. Now you could also have another arc that connects JK, this is the minor arc. It is the shortest way along the circle to connect J and K, but you could also go the other way around. You could also have this thing that goes all the way around the circle. And we would call that the major arc. And normally when you specify a major arc, just to show that you're going the long way around, it's not the shortest way to get between J and K, you'll often specify another point that you're going through. So for example, this major arc we could specify we start at J, we went through-- we could have said U, T, or S, but I'll put T right over there-- we went through T and then we went all the way to K. And so this specifies the major arc and this thing could have been the same thing as if I wrote JUK, these are specifying the same thing, or JSK. So there's multiple ways to specify this major arc right over here. But the one thing I make clear is, is that the minor arc is the shortest distance, so this is the minor arc, and the longer distance around is the major arc. And I'll leave you there and maybe the next few videos we'll start playing with some of this notation a little bit more.

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Circles glossary (video) | Circle basics | Khan Academy

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Let's start again with a point. Let's call that point point A. And what I'm curious about is all of the points on my screen right over here, that are exactly 2 centimeters away from A. So 2 centimeters on my screen is about that far.