lesson 6.3 congruent polygons and circles pp. 220-224
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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. - PowerPoint PPT PresentationTRANSCRIPT
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