Lesson 6.3 Congruent Polygons and Circles pp. 220-224

Lesson 6.3Congruent Polygons and

Circlespp. 220-224

Objectives:1. To define congruent polygons and

congruent circles.2. To use correct notation and criteria

for congruent polygons.

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.

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.

Definition

A

F

C

E

B

DABC DEF

Are ABC & DEF congruent?

Given ABC XYZ

AB 1. YX 2. XY3. ZY 4. XZ

A

B

C X

Y

Z

B 1. X 2. Y3. Z

Given ABC XYZ

A

B

C X

Y

Z

CBA 1. XYZ 2. YZX3. ZYX 4. XZY

Given ABC XYZ

A

B

C X

Y

Z

ACB 1. XYZ 2. YZX3. ZYX 4. XZY

Given ABC XYZ

A

B

C X

Y

Z

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

Definition

Theorem 6.9Triangle congruence is an equivalence relation.

Remember, an equivalence relation is a relation that is reflexive, symmetric, and

transitive.

Theorem 6.10Circle congruence is an equivalence relation.

Theorem 6.11Polygon congruence is an equivalence relation.

Homeworkpp. 223-224

►A. ExercisesWrite the correct triangle congruence statement for each pair.

1.

A PB

C

Q

L

►A. ExercisesWrite the correct triangle congruence statement for each pair.

5. U

P A T

K H

►A. ExercisesName the congruent triangles using correct notation.

9. TSI

I T

S

N D

A

►A. ExercisesName the congruent corresponding parts of the congruent triangles.

11. QMN LPS

►B. ExercisesUse the figure for exercises 14-17.14. Why are the angles at B congruent?

A C

B

XZ

►B. ExercisesUse the figure for exercises 14-17.15. Why is B the midpoint of CZ?

A C

B

XZ

►B. ExercisesUse the figure for exercises 14-17.16. Name the congruent triangles.

A C

B

XZ

■ Cumulative ReviewMatch. Be as specific as possible.21. A. Acute & equilateral

B. Acute & isoscelesC. Acute & scaleneD. Right & equilateralE. Right & isoscelesF. Right & scaleneG. Obtuse & equilateralH. Obtuse & isoscelesI. Obtuse & scalene

■ Cumulative ReviewMatch. Be as specific as possible.22. A. Acute & equilateral

B. Acute & isoscelesC. Acute & scaleneD. Right & equilateralE. Right & isoscelesF. Right & scaleneG. Obtuse & equilateralH. Obtuse & isoscelesI. Obtuse & scalene

■ Cumulative ReviewMatch. Be as specific as possible.23. A. Acute & equilateral

B. Acute & isoscelesC. Acute & scaleneD. Right & equilateralE. Right & isoscelesF. Right & scaleneG. Obtuse & equilateralH. Obtuse & isoscelesI. Obtuse & scalene

■ Cumulative ReviewMatch. Be as specific as possible.24. A. Acute & equilateral

B. Acute & isoscelesC. Acute & scaleneD. Right & equilateralE. Right & isoscelesF. Right & scaleneG. Obtuse & equilateralH. Obtuse & isoscelesI. Obtuse & scalene

■ Cumulative Review25. Which two choices describe impossible

triangles?A. Acute & equilateralB. Acute & isoscelesC. Acute & scaleneD. Right & equilateralE. Right & isoscelesF. Right & scaleneG. Obtuse & equilateralH. Obtuse & isoscelesI. Obtuse & scalene