1. Congruent Polygons and Circles
Lesson 6.3
Congruent Polygons and Circles pp

2. Objectives: 1. To define congruent polygons and congruent circles.
2. To use correct notation and criteria for congruent polygons.

3. Remember, segments are not equal when they have the same measure, they are congruent. The symbol for congruence is . The symbol  is used for all congruent figures, not just for segments and angles.

4. Definition Congruent circles are circles with congruent radii.
Congruent polygons are polygons that have three properties: 1) same number of sides, 2) corresponding sides are congruent, and 3) corresponding angles are congruent.

5. A
Are ABC & DEF congruent? B C F E D
ABC  DEF

6. Given ABC  XYZ A B C X Y Z
AB 
1. YX 2. XY
3. ZY 4. XZ

7. Given ABC  XYZ A B C X Y Z
B 
1. X 2. Y
3. Z

8. Given ABC  XYZ A B C X Y Z
CBA 
1. XYZ 2. YZX
3. ZYX 4. XZY

9. Given ABC  XYZ A B C X Y Z
ACB 
1. XYZ 2. YZX
3. ZYX 4. XZY

10. Definition
Congruent triangles are triangles in which corresponding angles and corresponding sides are congruent.

11. Theorem 6.9
Triangle congruence is an equivalence relation.

12. Remember, an equivalence relation is a relation that is reflexive, symmetric, and transitive.

13. Theorem 6.10
Circle congruence is an equivalence relation.

14. Theorem 6.11
Polygon congruence is an equivalence relation.

15. Homework pp

16. Write the correct triangle congruence statement for each pair. 1.
►A. Exercises
Write the correct triangle congruence statement for each pair. 1. A P B C Q L

17. Write the correct triangle congruence statement for each pair. 5.
►A. Exercises
Write the correct triangle congruence statement for each pair. 5. U P A T K H

18. Name the congruent triangles using correct notation. 9. TSI
►A. Exercises
Name the congruent triangles using correct notation.
9. TSI N D I T A S

19. ►A. Exercises
Name the congruent corresponding parts of the congruent triangles.
11. QMN  LPS

20. Use the figure for exercises 14-17.
►B. Exercises
Use the figure for exercises
14. Why are the angles at B congruent? A C B X Z

21. Use the figure for exercises 14-17. 15. Why is B the midpoint of CZ?
►B. Exercises
Use the figure for exercises
15. Why is B the midpoint of CZ? A C B X Z

22. Use the figure for exercises 14-17. 16. Name the congruent triangles.
►B. Exercises
Use the figure for exercises
16. Name the congruent triangles. A C B X Z

23. ■ Cumulative Review 21. A. Acute & equilateral
Match. Be as specific as possible.
21. A. Acute & equilateral
B. Acute & isosceles
C. Acute & scalene
D. Right & equilateral
E. Right & isosceles
F. Right & scalene
G. Obtuse & equilateral
H. Obtuse & isosceles
I. Obtuse & scalene

24. ■ Cumulative Review 22. A. Acute & equilateral
Match. Be as specific as possible.
22. A. Acute & equilateral
B. Acute & isosceles
C. Acute & scalene
D. Right & equilateral
E. Right & isosceles
F. Right & scalene
G. Obtuse & equilateral
H. Obtuse & isosceles
I. Obtuse & scalene

25. ■ Cumulative Review 23. A. Acute & equilateral
Match. Be as specific as possible.
23. A. Acute & equilateral
B. Acute & isosceles
C. Acute & scalene
D. Right & equilateral
E. Right & isosceles
F. Right & scalene
G. Obtuse & equilateral
H. Obtuse & isosceles
I. Obtuse & scalene

26. ■ Cumulative Review 24. A. Acute & equilateral
Match. Be as specific as possible.
24. A. Acute & equilateral
B. Acute & isosceles
C. Acute & scalene
D. Right & equilateral
E. Right & isosceles
F. Right & scalene
G. Obtuse & equilateral
H. Obtuse & isosceles
I. Obtuse & scalene

27. ■ Cumulative Review
25. Which two choices describe impossible triangles?
A. Acute & equilateral
B. Acute & isosceles
C. Acute & scalene
D. Right & equilateral
E. Right & isosceles
F. Right & scalene
G. Obtuse & equilateral
H. Obtuse & isosceles
I. Obtuse & scalene