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

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

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

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

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

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

7. A B C D E F

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

9. Congruent Angles
Congruent angles are angles with the same measure.

10. Congruent Segments
Congruent segments are segments with the same length.

11. congruence symbol

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

13. A B C D E F

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

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

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

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

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

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

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

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

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

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

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

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

26. scale factor—ratio of corresponding dimensions in similar figures

27. Example 2 RST ~ XYZ. Use a proportion to find XY. Y S 10 15 9 X 12 Z18 R T

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

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

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

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

32. D C 8 6 A F B E 40

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

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

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

36. Example Assume the two parallelograms are similar. FG = 8 12 B C F G 96 A D E
FG = 8

37. Example Assume the two parallelograms are similar. AE = 4 12 B C F G 96 A D E
AE = 4

38. Example If the diagonal AC = 15, what is the length of EG? 10 12 B C F9 6 A D E 10

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