Congruent Polygons and Circles

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Presentation transcript:

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

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.

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

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

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

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

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

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

Theorem 6.9 Triangle congruence is an equivalence relation.

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

Theorem 6.10 Circle congruence is an equivalence relation.

Theorem 6.11 Polygon congruence is an equivalence relation.

Homework pp. 223-224

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

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

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

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

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

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

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

■ 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

■ 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

■ 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

■ 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

■ 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