Lesson 6.3 Congruent Polygons and Circles pp. 220-224
description
Transcript of Lesson 6.3 Congruent Polygons and Circles pp. 220-224
![Page 1: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/1.jpg)
Lesson 6.3Congruent Polygons and
Circlespp. 220-224
![Page 2: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/2.jpg)
Objectives:1. To define congruent polygons and
congruent circles.2. To use correct notation and criteria
for congruent polygons.
![Page 3: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/3.jpg)
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.
![Page 4: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/4.jpg)
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
![Page 5: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/5.jpg)
A
F
C
E
B
DABC DEF
Are ABC & DEF congruent?
![Page 6: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/6.jpg)
Given ABC XYZ
AB 1. YX 2. XY3. ZY 4. XZ
A
B
C X
Y
Z
![Page 7: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/7.jpg)
B 1. X 2. Y3. Z
Given ABC XYZ
A
B
C X
Y
Z
![Page 8: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/8.jpg)
CBA 1. XYZ 2. YZX3. ZYX 4. XZY
Given ABC XYZ
A
B
C X
Y
Z
![Page 9: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/9.jpg)
ACB 1. XYZ 2. YZX3. ZYX 4. XZY
Given ABC XYZ
A
B
C X
Y
Z
![Page 10: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/10.jpg)
Congruent triangles are triangles in which corresponding angles and corresponding sides are congruent.
Definition
![Page 11: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/11.jpg)
Theorem 6.9Triangle congruence is an equivalence relation.
![Page 12: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/12.jpg)
Remember, an equivalence relation is a relation that is reflexive, symmetric, and
transitive.
![Page 13: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/13.jpg)
Theorem 6.10Circle congruence is an equivalence relation.
![Page 14: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/14.jpg)
Theorem 6.11Polygon congruence is an equivalence relation.
![Page 15: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/15.jpg)
Homeworkpp. 223-224
![Page 16: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/16.jpg)
►A. ExercisesWrite the correct triangle congruence statement for each pair.
1.
A PB
C
Q
L
![Page 17: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/17.jpg)
►A. ExercisesWrite the correct triangle congruence statement for each pair.
5. U
P A T
K H
![Page 18: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/18.jpg)
►A. ExercisesName the congruent triangles using correct notation.
9. TSI
I T
S
N D
A
![Page 19: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/19.jpg)
►A. ExercisesName the congruent corresponding parts of the congruent triangles.
11. QMN LPS
![Page 20: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/20.jpg)
►B. ExercisesUse the figure for exercises 14-17.14. Why are the angles at B congruent?
A C
B
XZ
![Page 21: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/21.jpg)
►B. ExercisesUse the figure for exercises 14-17.15. Why is B the midpoint of CZ?
A C
B
XZ
![Page 22: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/22.jpg)
►B. ExercisesUse the figure for exercises 14-17.16. Name the congruent triangles.
A C
B
XZ
![Page 23: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/23.jpg)
■ 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
![Page 24: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/24.jpg)
■ 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
![Page 25: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/25.jpg)
■ 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
![Page 26: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/26.jpg)
■ 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
![Page 27: Lesson 6.3 Congruent Polygons and Circles pp. 220-224](https://reader031.fdocuments.in/reader031/viewer/2022012922/56816194550346895dd13640/html5/thumbnails/27.jpg)
■ 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