Exercise Compare by using >, <, or =. 9 12 11 16 >

Exercise Compare by using >, <, or =. 12 18 8 12 =

Exercise Compare by using >, <, or =. 1628 13 21 <

Exercise Solve the proportion. x 15 16 12 = x = 20

Exercise Solve the proportion. 5 7 2 d = d = = 2 = 2.8 14 5 4 5

Congruent Polygons Congruent polygons are polygons with the same size and shape.

A B C D E F

same place in different figures corresponding angles same place in different figures corresponding sides

Congruent Angles Congruent angles are angles with the same measure.

Congruent Segments Congruent segments are segments with the same length.

congruence symbol

Corresponding angles are congruent (have the same measure). A D B E C F Corresponding angles are congruent (have the same measure).

A B C D E F

Corresponding sides are congruent (have the same length). AC DF AB DE BC EF Corresponding sides are congruent (have the same length).

Example 1 RST XYZ. Complete each statement. S Y R T Z X R X

Example 1 RST XYZ. Complete each statement. S Y R T Z X S Y

Example 1 RST XYZ. Complete each statement. S Y R T Z X T Z

Example 1 RST XYZ. Complete each statement. S Y R T Z X RT XZ

Example 1 RST XYZ. Complete each statement. S Y R T Z X RS XY

Example 1 RST XYZ. Complete each statement. S Y R T Z X ST YZ

Similar Polygons Similar polygons are polygons that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.”

Theorem If two polygons are similar, then the corresponding angles are congruent and the lengths of the corresponding sides are proportional.

B Corresponding Angles 6 9 A D 12 A C E B E 6 4 C F D 8 F

B Corresponding Sides 6 9 AB DE 12 A C E AC DF 6 4 BC EF D 8 F

AB DE = 6 4 3 2 AC DF = 12 8 3 2 BC EF = 9 6 3 2

scale factor—ratio of corresponding dimensions in similar figures

Example 2 RST ~ XYZ. Use a proportion to find XY. Y S 10 15 9 X 12 Z 18 R T

XY RS = XZ RT 2 3 XY 9 = 3(XY) = 18 3 XY = 6

Example ABC ~ FED. Complete the ratio. D C 8 6 A F B E AB FE = FD AC

Example ABC ~ FED. If BC = 9, what is ED? D C 8 6 A F B E 12

Example ABC ~ FED. If the perimeter of ABC is 30, what is the perimeter of FED?

D C 8 6 A F B E 40

Example ABC ~ FED. If m A = 85° and m E = 30°, what is the m C? 65° D

Example Are PQR and JKL similar? L Q 8 6 J 18 12 P 12 8 no K R

Example What length of PQ would make them similar? 9 L Q 8 6 18 J 12 P

Example Assume the two parallelograms are similar. FG = 8 12 B C F G 9 6 A D E FG = 8

Example Assume the two parallelograms are similar. AE = 4 12 B C F G 9 6 A D E AE = 4

Example If the diagonal AC = 15, what is the length of EG? 10 12 B C F 9 6 A D E 10

Example What is the perimeter of EFGD? 12 B C F G 9 6 A D E 28