CHAPTER+ON+Similar+Shapes

[|Lesson 8.1] [|Lesson 8.2] [|Lesson 8.3] [|Lesson 8.4] [|Lesson 8.5]



Dilations and Scale Factors
dilation- is like a transformation but the size changes too. Like the circles below. [|link to site]

scale factor-When you have a dilation on the coordinate plane, each point (x,y) is multiplied by a number. We'll use n. Then you get (nx,ny). n is called the scale factor. See below. Assume the real car is =1. The model is 1/32 it's size in all dimensions. So the scale factor one way is 1/32 and the other way it is 32/1 or 32. [|creative commons license] Scale model of a city http://www.flickr.com/photos/blakeisrael/160233628/ center of dilation- The origin is the center of dilation on the coordinate grid.

contraction- something reduced by a dilation [|CC]

expansion- something increased by a dilation [|See pics rights]



Similar Polygons
photo by Eric Gjerde copyright link on picture __similar__- notice the shapes of the light hexagon and the dark hexagon are the __same shape__, but __different sizes__.

proportional

proportion- the sides of similar objects are proportional

Polygon similarity Postulate- If two polygons are similar then
 * each pair of corresponding angles is congruent
 * Each pair of corresponding sides is proportional

How proportions work 1/2=3/6



Triangle Similarity
AA similarity

SSS similarity

SAS similarity



What is it about the letter "A"?
Side splitting theoren 

How do you measure that?
Use triangle similarity to measure distances indirectly.