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Parallel Lines

Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember:

Always the same distance apart and never touching.

The red line is parallel to the blue line in each of these examples:

Parallel lines also point in the same direction.

Parallel lines have so much in common. It's a shame they will never meet!

Try it yourself:

Pairs of Angles

When parallel lines get crossed by another line (which is called a Transversal), you can see that many angles are the same, as in this example:

These angles can be made into pairs of angles which have special names.

Click on each name to see it highlighted:

Now play with it here. Try dragging the points, and choosing different angle types. You can also turn "Parallel" off or on:

Testing for Parallel Lines

Some of those special pairs of angles can be used to test if lines really are parallel:

Examples

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Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember: The red line is parallel to the blue line in each of these examples: Parallel lines also point in the same direction. Parallel lines have so much in common.

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Polygons Degrees (Angle) Angles Around a Point Interior Angles of Polygons Interior Angles Exterior Angles 2D Shapes Geometry Index

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An Interior Angle is an angle inside a shape. Example: ...

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Exterior Angles of Polygons Interior Angles Interior Angles of Polygons Supplementary Angles Angles On a Straight Line Straight Angle Degrees (Angle) Geometry Index

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Interior Angles of Polygons Exterior Angles Supplementary Angles Complementary Angles Angles On a Straight Line Angles Around a Point Degrees (Angle) Geometry Index

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These are important to learn!

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Symbols save time and space when writing. Here are the most common geometrical symbols:

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links at bottom of the page

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When two angles add to 90°, we say they "Complement" each other. Complementary comes from Latin completum meaning "completed" ... because the right angle is thought of as being a complete angle.

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links to questions at bottom of page

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These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:

Notice that together they make a straight angle.

But the angles don't have to be together.

These two are supplementary because
60° + 120° = 180°

Play With It ...

(Drag the points)

images/geom-comp-supp.js?mode=supp

When the two angles add to 180°, we say they "Supplement" each other. comes from Latin supplere, to complete or "supply" what is needed

Complementary vs Supplementary

A related idea is Complementary Angles, they add up to 90°

How to remember which is which? Well, alphabetically they are:

Complementary add to 90°

Supplementary add to 180°

You can also think:

"C" of Complementary is for "Corner" (a Right Angle), and

"S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

when you are right you get a compliment (sounds like complement)

"supplement" (like a vitamin supplement) is something extra, so is bigger

817, 1804, 5232, 5234, 818, 3303, 1805, 3304, 5235, 5236

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Two Angles are Supplementary when they add up to 180 degrees.

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links to questions down the bottom of page

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Links to questions at bottom of the page

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This method can be used for several angles on one side of a straight line.

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There is a link to questions at the bottom of the page.

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Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.

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Classify the triangles by their angles

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...and yes another song but this one has dancing cats

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...and yes another song but this one has dancing cats

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The BEST Angles Math Song! (with bonus DANCING CATS!)

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Year 9 P.7

Year 10 F.4 Use the info on the padlet page tp help you.

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Practising Year 9 maths: 'Identify complementary, supplementary, vertical, adjacent and congruent angles'

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Fun maths practice! Improve your skills with free problems in 'Identify complementary, supplementary, vertical, adjacent and congruent angles' and thousands of other practice lessons.

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Equilateral, Isosceles and Scalene

There are three special names given to triangles that tell how many sides (or angles) are equal.

There can be 3, 2 or no equal sides/angles:

How to remember? Alphabetically they go 3, 2, none:

Equilateral: "equal"-lateral (lateral means side) so they have all equal sides

Isosceles: means "equal legs", and we have two legs, right? Also iSOSceles has two equal "Sides" joined by an "Odd" side.

Scalene: means "uneven" or "odd", so no equal sides.

What Type of Angle?

Triangles can also have names that tell you what type of angle is inside:

Has a right angle (90°)

Combining the Names

Sometimes a triangle will have two names, for example:

Play With It ...

Try dragging the points around and make different triangles:

You might also like to play with the Interactive Triangle.

Angles

The three interior angles always add to 180°

Perimeter

The perimeter is the distance around the edge of the triangle: just add up the three sides:

Area

The area is half of the base times height.

"b" is the distance along the base

"h" is the height (measured at right angles to the base)

Area = ½ × b × h

The formula works for all triangles.

Note: a simpler way of writing the formula is bh/2

Example: What is the area of this triangle?
(Note: 12 is the height, not the length of the left-hand side)
Height = h = 12

Base = b = 20

Area = ½ × b × h = ½ × 20 × 12 = 120

The base can be any side, Just be sure the "height" is measured at right angles to the "base":

(Note: You can also calculate the area from the lengths of all three sides using Heron's Formula.)

Why is the Area "Half of bh"?

Imagine you "doubled" the triangle (flip it around one of the upper edges) to make a square-like shape (a parallelogram) which can be changed to a simple rectangle:

THEN the whole area is bh, which is for both triangles, so just one is ½ × bh.

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There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles: How to remember? Alphabetically they go 3, 2, none: Equilateral: "equal"-lateral (lateral means side) so they have all equal sides Isosceles: means "equal legs", and we have two legs, right?

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To help you remember the names of angles

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To help you remember the names of angles