Geometry

=Types of Angles=

> = = =Properties of Triangles= Triangles are one of the most fundamental geometric shapes and have a variety of often studied properties relating to their
 * A cute:less than 90o. Angle number 1 is an acute angle
 * Obtuse: greater then90o. Angle number 2 is obtuse.
 * When 2 angles add up to 90o these are called complementary angles. Angles 1 and 2 are complementary.
 * [[image:http://www.mathwarehouse.com/geometry/angle/images/picture-adjacent-angles.gif width="207" height="95" align="right" caption="Picture of adjacent angles"]] ||
 * A djacent angles : two coplanar angles with a common side, a common vertex, and no common interior points. Angles 3 and 4 are adjacent angles. They are also suplementray angles as they add up to 180o.
 * Angles on a straight line add up to 180o. Angles 3 and 4 add up to 180o.
 * So angles 3 and 4 are linear pair of angles: angles that are supplementary and adjacent and add up to 180o.


 * ===Interior Angles (angles on the inside) add up to 180°===
 * ===This may be one the most well known mathematical rule--//The sum of all 3 interior angles in a triangle is 180°.// As you can see from the picture below, if you add up all of the angles in a triangle the sum must equal 180°.===

No matter how you position the three sides of the triangle, the total degrees of all [|interior angles](the three angles inside the triangle) is always 180°. Try the following exercises in this PDF. Click on the link =**What is the difference between interior and exterior angles of a triangle?**= > ====This question is answered by the picture below. You create an exterior angle by extending any side of the triangle. As you can see, we now have a straight line. Straight lines add up to 180°, so A + D = 180°. C + B also = D.==== = = =An exterior angle(D) equals the sum of the remote interior angles (B and C).=

T Try the following worksheet on this. Some exercises require algebra. Click on the link

[[file:remote-exterior-interior-angles.pdf]]
> Practice lining up and reading a protractor while you measure a set of angles. The angles may range from 0Â° to 180Â°. The interactive protractor is already lined up with the vertex of each angle but you will have to rotate the protractor into the proper position. The margin of error is only 1Â° and you must report measurement to the nearest whole number.
 * ==Relationship between measurement of the sides and angles in a Triangle: The largest interior angle and side are opposite each other. The same rule applies to the smallest sized angle and side and the middle sized angle and side==
 * the largest interior angle is **opposite** the largest side.
 * the smallest interior angle is **opposite** the smallest side
 * the middle-sized interior angle is **opposite** the middle-sized side
 * =[|Measuring Angles with a Protractor]=
 * Angles can be measured using a protractor. Click on the following link and practise protractor use.
 * [|Using a Protractor]

[|What’s My Angle?]
[] Investigate angles and the use of protractors. =Transversals and angles of intersecting lines=

Formula for alternate-interior, same side interior, exterior and corresponding
When a transversal intersects two lines a series of angles are formed.

**A transversal creates several distinct types of angles.** The red line on the left is a transversal that intersects line a and line b.

Corresponding Angles
Corresponding angles are the angle pairs that are in the same position. The corresponding angle pairs are color coded on the left.
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]1 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]5
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]3 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]7
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]4 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]8
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]2 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]6 ||==

Alternate Exterior Angles.
Alternate Exterior angles are the angle pairs that are on the outsides of the two lines (the exterior) and on opposite (or alternate sides) of the transversal. The Alternate Exterior Angle pairs are illustrated on the left.
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]1 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]8
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]2 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]7

Alternate Interior Angles (in greater Depth)
Alternate Interior angles are the angle pairs that are on the insides of the two lines (the interior) and on opposite (or alternate sides) of the transversal. The Alternate Interior Angle pairs are pictured on the left.
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]3 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]6
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]4 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]5

Same Side Interior (in greater Depth)

Same Side Interior angles
Same Side Interior angles are the angle pairs that are on the insides of the two lines (the interior) and on the same side of the transversal. The Same Side Interior Angle pairs are pictured on the left.
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]3 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]5
 * [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]4 and [[image:http://www.mathwarehouse.com/images/angle_symbol_CCCCFF.jpg width="24" height="22"]]6

Interactives:

Exterior Angle of a Triangle


Try this interactive out at the following link:

http://www.mathwarehouse.com/geometry/triangles/angles/remote-exterior-and-interior-angles-of-a-triangle.php#demoRemoteExteriorAngle Vertical Angles

Try this interactive out at the following link:

http://www.mathwarehouse.com/geometry/angle/interactive-vertical-angles.php

Parallel Lines Angles

 media type="youtube" key="-BPdBfwFgUM" width="420" height="315"

media type="youtube" key="c1CcLH6VhuI" width="420" height="315"media type="youtube" key="h7TYeYRM-xY" width="420" height="315" As well as demonstrating these to a class using a Projector, it is also possible to make a video tutorial while using the product. Use Jing with Screencast for free, or else purchase the excellent Camtasia product for making narrated video screen captures. The video below has been made by Khan Academy, and is available on YouTube

To access a full list of all the Interactives at Math Warehouse, click the link below: http://www.mathwarehouse.com/interactive/ = Games =

[| http://apod.nasa.gov/apod/ap100929.html][|nasa]
WCYDWT ? This image is a great stimulus to build a similar triangle problem. Students could use the internet to find out various dimensions and demonstrate or calculate a missing variable such as: how high was the plane flying. See also [] and forum for more details. Could load image into GeoGebra for more accurate modelling

[|Alien Angles]
[][|Alien Angles]

[|Asteroids]
[][|Asteriods] Practice estimating angles with this fun geometry game.

[|Angle Activities]
[][|Angle Activities] 20 interactive investigations using a protractor.

[|Banana Hunt]
[][|Banana Game] Move the monkey to match the angle given, you are rewarded for your accuracy with bananas.

[|Pyramid Panic - Mangahigh]
[] In this geometry game set in Ancient Egypt, you have been prematurely mummified and entombed within a pyramid. The object of this maths game is to help your mummy to escape to freedom, by solving geometry puzzles and building a path across the voids of the pyramid`s burial chambers. Unfortunately, the pyramid contains many evil characters such as skull bats, skeleton thieves and a ferocious mystical Egyptian demon called Ammit, all of whom are intent on preventing your escape. Stay ahead of Ammit and zap other enemies with your Ankh Sceptre while you select shapes and build a path out of the tomb.

[|Bearings]
[] [|Bearings] Rescue the waving man by telling the ship what bearing it should sail at. Avoid the floating icebergs!

[|Flip Card - Angle Types]
[] [|Flip Card] Concentration game for angle types.

[|Kung Fu Angles]
[] Use a knowledge of angles to defeat the enemy.[|Kung Fu Angles]