Similar Polygons

Informal Definition of Similar Figures Two figures are similar if they have the same shape. (They do not necessarily have the same size.)

Formal Definition of Similar Polygons Two polygons are similar iff their corresponding angles are congruent,and (lengths of) corresponding sides are proportional. C A B E D F  A   D  B   E  C   F

Proportional (Lengths of) sides are proportional iff ratios of (lengths of) corresponding sides are equal. For example: so the sides are proportional. 5 9 7 18 10 14 C A B Z Y X

Scale Factor from ABC to _____ is____. from ZYX to ABC ZYX 2 1/2 The ratio of corresponding sides of similar polygons. Example The scale factor from ABC to _____ is____. from ZYX to ABC ZYX 7 9 5 18 10 14 C A B Z Y X 2 1/2

Naming Similar Polygons **Must match the corresponding letters**

Applying the Definition - Angles **Must match the corresponding vertices**

Applying the Definition - Sides **Must match the corresponding sides** Proportional means all of the ratios are equal!

Find the lengths of the missing sides. Example 1 18 14 28 24 8 Given Find the lengths of the missing sides.

Example 1 Step 1: Write out a proportion of for the sides. 14 8 18 24 28 24 8 Given Find AC Step 1: Write out a proportion of for the sides. (Be sure to match up corresponding letters!)

Step 2: Replace the sides with the lengths from the problem. Example 1 18 14 28 24 8 Given Find the lengths of the missing sides. Step 2: Replace the sides with the lengths from the problem.

Step 3: Cross-multiply and solve. Example 1 18 14 28 24 8 Given Find the lengths of the missing sides. Step 3: Cross-multiply and solve.

You should be able to find CD and BD as well! Example 1 18 14 28 24 8 Given You should be able to find CD and BD as well!

Example 2 14 8 18 24 28 Given Find the scale factor of ABDC to RPSQ Remember the scale factor is same as the ratio of the sides. Always put the first polygon mentioned in the numerator. The scale factor of ABDC to RPSQ is

x = 7.5 y = 10 z = 15 ABCD  EFGH. Solve for x, y and z. Example 3 5 z x 10 y 15 30 20 B C A D F G E H ABCD  EFGH. Solve for x, y and z. Step 1: Write a proportion using names of sides. Step 2: Substitute values. Step 3: Cross-multiply to solve. Step 4: Repeat to find other values. Type notes here x = 7.5 y = 10 z = 15

Dilations and Scale Factor A dilation is a transformation that changes the size of an object. The scale factor is the ratio of the lengths of the corresponding sides of two similar polygons. It indicates the relative size of one polygon compared the another.

Are congruent triangles similar? What is the scale factor between two congruent triangles?