# data[].attributes.body
Click "View" to see a web page all about Quadrilaterals. 

# data[].attributes.attachment_link.readable_text
Quadrilateral just means "four sides"
( quad means four, lateral means side).

A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

Try it Yourself

geometry/images/geom-quad.js?mode=choose
(Also see this on Interactive Quadrilaterals)
Properties

A quadrilateral has:

four sides (edges)

four vertices (corners)

interior angles that add to 360 degrees:

Try drawing a quadrilateral, and measure the angles. They should add to 360°

Types of Quadrilaterals

There are special types of quadrilateral:

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms. See below for more details.

Let us look at each type in turn:

The Rectangle

the little squares in each corner mean "right angle"
A rectangle is a four-sided shape where every angle is a right angle (90°).

Also opposite sides are parallel and of equal length.

the little squares in each corner mean "right angle"
The Square

A square has equal sides (marked "s") and every angle is a right angle (90°)

Also opposite sides are parallel.

A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

The Rhombus

A rhombus is a four-sided shape where all sides have equal length (marked "s").

Also opposite sides are parallel and opposite angles are equal.

Another interesting thing is that the diagonals (dashed lines) meet in the middle at a right angle. In other words they "bisect" (cut in half) each other at right angles.

A rhombus is sometimes called a rhomb or a diamond.

The Parallelogram

A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same).

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

A parallelogram with:

all sides equal and

angles "A" and "B" as right angles

is a square!

The Trapezoid (UK: Trapezium)

A trapezoid (called a trapezium in the UK) has a pair of opposite sides parallel.

And a trapezium (called a trapezoid in the UK) is a quadrilateral with NO parallel sides:

An Isosceles trapezoid, as shown above, has left and right sides of equal length that join to the base at equal angles.

The Kite

Hey, it looks like a kite (usually).

It has two pairs of sides:

Each pair is made of two equal-length sides that join up.

Also:

the angles where the two pairs meet are equal.

the diagonals, shown as dashed lines above, meet at a right angle.

one of the diagonals bisects (cuts equally in half) the other.

... and that's it for the special quadrilaterals.

Irregular Quadrilaterals

The only regular (all sides equal and all angles equal) quadrilateral is a square. So all other quadrilaterals are irregular.

The "Family Tree" Chart

Quadrilateral definitions are inclusive.
(We don't say "Having all 90° angles makes it a rectangle except when all sides are equal then it is a square.")
Example: a square is also a rectangle.

So we include a square in the definition of a rectangle.

This may seem odd, as in daily life we think of a square as not being a rectangle ... but in mathematics it is.

Using the chart below we can answer such questions as:

Is a Square a type of Rectangle? (Yes)

Is a Rectangle a type of Kite? (No)

Complex Quadrilaterals

Oh Yes! when two sides cross over, we call it a "Complex" or "Self-Intersecting" quadrilateral, like these:

They still have 4 sides, but two sides cross over.

Polygon

A quadrilateral is a polygon. In fact it is a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a 5-sided polygon, and so on.

Play with Them

Now that you know the different types, you can play with the Interactive Quadrilaterals.

Other Names

A quadrilateral can sometimes be called:

a Quadrangle ("four angles"), so it sounds like "triangle"

a Tetragon ("four polygon"), so it sounds like "pentagon", "hexagon", etc.

621,622,623,624,763,764, 2128, 2129, 3230, 3231

# data[].attributes.attachment_link.description
Quadrilateral just means "four sides" ( quad means four, lateral means side). A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides. geometry/images/geom-quad.js?mode=choose (Also see this on Interactive Quadrilaterals) A quadrilateral has: four sides (edges) four vertices (corners) interior angles that add to 360 degrees: Try drawing a quadrilateral, and measure the angles.

# data[].attributes.body
Types of Quadrilaterals we need to know are these four sided figures: 

# data[].attributes.body
A 5 minute YouTube video on solving connected SIMILAR TRIANGLES. 

# data[].attributes.body
Triangles in Patchwork Quilting Embroidery. 

# data[].attributes.body
Here is a PowerPoint with Sound that goes through the main Polygon shapes. 
Use "Page Down" key to advance each slide. 

# data[].attributes.body
Here is a Powerpoint on Polygons (that has sound). 
Turn your speakers on, and use the "Page Down" key to go forward. 

# data[].attributes.body
The Web Page link below shows examples of POLYGON ANGLES using the (n-2)x180 formula, and also has the names of most Polygons.  

# data[].attributes.body
Here are some interesting triangles present in Crystals and jewelry. 

# data[].attributes.body
The following Powerpoint covers polygon definitions, Triangles, Quadrilaterals, and all other shapes as well. (Use "Page-Down" key) to do the slides. 

# data[].attributes.body
Names of Polygons and Example of INTERIOR ANGLE SUM for any polygon = (n-2)x180 where n = no of sides. 

# data[].attributes.body
INTERIOR ANGLES OF POLYGONS - The web page link below explains where the   (n-2) x 180 formula comes from. 

# data[].attributes.body
Triangles and Angles are important in studying Biomechanics, Robotics, and Human Movement in Sports.

# data[].attributes.body
Here is an XLS spreadsheet that has been programmed to help identify Triangle Types. Give it a Try and see how you go. 

# data[].attributes.body
Triangles provide great strength to the roll cages of Rally and Racing Cars. 
 

# data[].attributes.body
Triangles are a very important structural component in the design and building of Bridges.

# data[].attributes.body
CONGRUENT Triangles have all sides equal, and all three angles identical. This is shown in the diagram below. 

# data[].attributes.body
Polygon Types - The birth of the "Rhombus" :) 

# data[].attributes.body
An interesting set of Triangle Types :) 

# data[].attributes.body
The following YouTube video is on Similar Triangles Problem Solving, and goes for around 5 minutes. 

# data[].attributes.body
The following 3 minute YouTube video explains Similar Triangles and finding corresponding SIDES on them. 

# data[].attributes.attachment_link.title
Similar Triangles - MathHelp.com - Geometry Help

# data[].attributes.body
The following 3 minute YouTube video explains Similar Triangles and finding corresponding ANGLES in them. 

# data[].attributes.attachment_link.title
Similar Triangles - MathHelp.com - Geometry Help

# data[].attributes.body
Here is a PowerPoint on QUADRILATERALS and Angles from "Monica". Use the "Page-Up" and "Page-Down" keys to go back to slides, if you need to stop the animation.

# data[].attributes.body
Parallel Lines and their Angles. YouTube video 10 minutes. 

# data[].attributes.attachment_link.title
Angles (part 3) | Angles and intersecting lines | Geometry | Khan Academy

# data[].attributes.body
Complementary and Supplementary Angles You Tube Video - 9 minutes.

# data[].attributes.attachment_link.title
Angles (part 2) | Angles and intersecting lines | Geometry | Khan Academy

# data[].attributes.body
Here is some end of University Level information about Triangle Properties. 
This will definitely NOT be on our Test !!

# data[].attributes.body
Here is a 2 minute YouTube of an Algebra Alternate angles problem. 

# data[].attributes.attachment_link.title
Alternate Interior Angles - MathHelp.com - Geometry Help

# data[].attributes.body
The following is a web Slideshare Presentation on Angles and Parallel Lines. 
Find and Click on "Get File" then "open", because Sshare is not ok in the wall. 

# data[].attributes.attachment_link.readable_text
Successfully reported this slideshow.

Download Now Download

Download to read offline

1. 1. LINE AND ANGLE RELATIONSHIPS Free powerpoints at http:// www.worldofteaching.com

2. 2. TYPES OF ANGLES <ul><li>Acute Angles have measures less than 90°. </li></ul><ul><li>Right Angles have measures equal to 90°. </li></ul><ul><li>Obtuse Angles have measures between 90° and 180°. </li></ul><ul><li>Straight Angles have measures equal to 180° </li></ul>

3. 3. PARALLEL LINES <ul><li>Def: Lines that do not intersect. Parallel lines are always the same distance apart. </li></ul><ul><li>Illustration: </li></ul><ul><li>Notation: l || m AB || CD </li></ul>l m A B C D

4. 4. PERPENDICULAR LINES <ul><li>Def: Lines that intersect to form a right angle. </li></ul><ul><li>Illustration: </li></ul><ul><li>Notation: m  n </li></ul><ul><li>Key Fact: 4 right angles are formed. </li></ul>m n

5. 5. <ul><li>Def: A line that intersects two lines at different points. </li></ul><ul><li>Illustration: </li></ul>Transversal t

6. 6. Vertical Angles <ul><li>Two angles that are opposite angles. </li></ul>1 2 3 4 5 6 7 8 t <ul><li>1   4 </li></ul><ul><li>2   3 </li></ul><ul><li>5   8 </li></ul><ul><li>6   7 </li></ul>

7. 7. Vertical Angles <ul><li>Find the measures of the missing angles </li></ul>125  ? ? 55  t

8. 8. Vertical Angles <ul><li>Find the measures of the missing angles </li></ul>125  55  t 55  125 

9. 9. Angle Relationships <ul><li>Complementary Angles are two angles whose sum is 90°. </li></ul><ul><li>Supplementary Angles are two angles whose sum is 180°. </li></ul><ul><li>Angles do not have </li></ul><ul><li>to be Adjacent to be Complementary or Supplementary. </li></ul><ul><li>Adjacent Angles </li></ul><ul><li>are two angles that share a common side. </li></ul>

10. 10. Supplementary Angles/ Linear Pair <ul><li>Two angles that form a line (sum=180  ) </li></ul><ul><li>5+  6=180 </li></ul><ul><li>6+  8=180 </li></ul><ul><li>8+  7=180 </li></ul><ul><li>7+  5=180 </li></ul><ul><li>1+  2=180 </li></ul><ul><li>2+  4=180 </li></ul><ul><li>4+  3=180 </li></ul><ul><li>3+  1=180 </li></ul>1 2 3 4 5 6 7 8 t

11. 11. Supplementary Angles/ Linear Pair <ul><li>Find the measures of the missing angles </li></ul>? 72  ? t 180 - 72

12. 12. Supplementary Angles/ Linear Pair <ul><li>Find the measures of the missing angles </li></ul>72  t 108  108  180 - 72

13. 13. Corresponding Angles <ul><li>Two angles that occupy corresponding positions. </li></ul>Top Left t Top Left Top Right Top Right Bottom Right Bottom Right Bottom Left Bottom Left <ul><li>1   5 </li></ul><ul><li>2   6 </li></ul><ul><li>3   7 </li></ul><ul><li>4   8 </li></ul>1 2 3 4 5 6 7 8

14. 14. Corresponding Angles <ul><li>Find the measures of the missing angles </li></ul>145  ? t 35 

15. 15. Corresponding Angles <ul><li>Find the measures of the missing angles </li></ul>145  t 35  145 

16. 16. Alternate Interior Angles <ul><li>Two angles that lie between parallel lines on opposite sides of the transversal </li></ul>t <ul><li>3   6 </li></ul><ul><li>4   5 </li></ul>1 2 3 4 5 6 7 8

17. 17. Alternate Interior Angles <ul><li>Find the measures of the missing angles </li></ul>82  ? t 98 

18. 18. Alternate Interior Angles <ul><li>Find the measures of the missing angles </li></ul>82  t 98  82 

19. 19. Alternate Exterior Angles <ul><li>Two angles that lie outside parallel lines on opposite sides of the transversal </li></ul>t <ul><li>2   7 </li></ul><ul><li>1   8 </li></ul>1 2 3 4 5 6 7 8

20. 20. Alternate Exterior Angles <ul><li>Find the measures of the missing angles </li></ul>120  ? t 60 

21. 21. Alternate Exterior Angles <ul><li>Find the measures of the missing angles </li></ul>120  t 60  120 

22. 22. Consecutive Interior Angles <ul><li>Two angles that lie between parallel lines on the same sides of the transversal </li></ul>t <ul><li>3 +  5 = 180 </li></ul><ul><li>4 +  6 = 180 </li></ul>1 2 3 4 5 6 7 8

23. 23. Consecutive Interior Angles <ul><li>Find the measures of the missing angles </li></ul>? t 135  180 - 135

24. 24. Consecutive Interior Angles <ul><li>Find the measures of the missing angles </li></ul>t 135  45  180 - 135

25. 25. This presentation is a modified version of the Slideshow: " Lines and Angles 2 " by Miss Patel. The original Slideshow Presentation can be found at www.worldofteaching.com

# data[].attributes.attachment_link.description
Successfully reported this slideshow. Download Now Download Download to read offline 1. LINE AND ANGLE RELATIONSHIPS Free powerpoints at http:// www.worldofteaching.com 2. TYPES OF ANGLES Acute Angles have measures less than 90°. Right Angles have measures equal to 90°. Obtuse Angles have measures between 90° and 180°.

# data[].attributes.body
The web page below, has an interactive setup, where we can click on Parallel Lines and see the Angles click on "interactive" at top to find a full size version.

# data[].attributes.attachment_link.readable_text
1. Home

2. Geometry

3. Parallel Lines & Transversal

4. Interactive Parallel Lines

Explore the rules on your own

Click and drag around the points below to explore and discover the rule for parallel lines cut by a transversal on your own. You can click and drag points A, B, and C.

You can create a customized shareable link (at bottom) that will remember the exact state of the app--which angles are selected and where the points are, so that you can share your it with others.

Drag Points Of The Lines To Start Demonstration

# data[].attributes.attachment_link.title
Interactive Corresponding, Alternate Exterior, and Alternate Interior Angles. Learn about the rule with this exploratory activity. Just Click and drag the points and discover!

# data[].attributes.attachment_link.description
Home Geometry Parallel Lines & Transversal Interactive Parallel Lines Explore the rules on your own Click and drag around the points below to explore and discover the rule for parallel lines cut by a transversal on your own. You can click and drag points A, B, and C.

# data[].attributes.body
Similar Triangles - Pt2
10 minute YouTube Video

# data[].attributes.attachment_link.title
Similar triangles (part 2) | Similarity | Geometry | Khan Academy

# data[].attributes.body
Similar Triangles - Pt1
10 minute YouTube Video

# data[].attributes.attachment_link.title
Similar triangles | Similarity | Geometry | Khan Academy

# data[].attributes.body
This might not teach that much Geometry, but could be good for a laugh or two. Video links to YouTube and is 6 mins 30 secs long. 

# data[].attributes.body
Here is a PowerPoint on Triangles and Polygons from "Mrs Martin". Use the "Page-Up" and "Page-Down" keys to go back to slides, if you need to stop the animation

# data[].attributes.body
Angles in Parallel Lines -Pt2
The webpage link here has the remaining angle types: 

# data[].attributes.body
Angles in Parallel Lines -Pt1
The webpage link here has some of the angle types: 

Note that "Congruent" means the angles are the exact same size in degrees

# data[].attributes.body
Triangles can be classified by either their SIDES or by their ANGLES. 

# data[].attributes.body
There are four main types of Triangles: Isosceles, Scalene, Equilateral, and Right Angled. 