Similarity and Transforms!


Translation: slide

Reflection: flip

Rotation: turn

Dilatation: enlargement or shrinkage based on scale factor.

Scale factor: the ratio of the lengths of 2 corresponding sides of 2 similar polygons

Similar Polygons!

In the picture below you have Triangle-WUV and Triangle-ZXY are they similar?

PLEASE NOTE THAT...If 2 polygons are similar, then their corresponding angles and the measures of their corresponding sides are proportional.

To find out if a figure is similar you must first identify the angles that are corresponding and determine if they are congruent in this case angles.

Polygons that have the same shape are called Similar polygons. In the above example triangle WUV is similar to triangle ZXY  is is written as WUV ~ ZXY.

Finding The Transforms!

Quadrilateral WXYZ is similar to Quadrilateral ABCD.

Choose 2 corresponding sides and determine what transforms will map one onto the other. If I chose corresponding sides AB/WX you would say the transforms used were a translation followed by a dilation.

Finding Missing Measures!

You can find missing measure is 2 simple methods.

Method 1!

Before you begin the process of finding the missing measures you must first find the scale factor. To find the scale factor of  quadrilateral ABCD to quadrilateral WXYZ take 2  corresponding sides that are not missing and put them into a proportion.It will look something like this CD/YZ= 10/15 or 2/3. So the length on polygon ABCD is 2/3 times as long as the corresponding length on polygon WXYZ. Let m represent the measure of XY.   write the equation---> m = 2/3(12)  m=18

Method 2!

Set up a proportion to find the missing measure. It will look a little something like this.

Write the proportion.----> XY/BC = YZ/CD

-XY=m, BC=12, YZ=15, CD=10 ----> m/12 = 15/10  

Find the cross products.---->m x 10 = 12 x 15

Simplify ---->10m= 180

Answer--->  M= 18


If you need extra help on simliar polygons of finding missing meaures this viedo may help.

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