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Five-Minute Check (over Lesson 4–2)
Then/Now
New Vocabulary
Key Concept: Definition of Congruent Polygons
Example 1: Identify Corresponding Congruent Parts
Example 2: Use Corresponding Parts of Congruent Triangles
Theorem 4.3: Third Angles Theorem
Example 3: Real-World Example: Use the Third Angles Theorem
Example 4: Prove that Two Triangles are Congruent
Theorem 4.4: Properties of Triangle Congruence
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Over Lesson 4–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 115
B. 105
C. 75
D. 65
Find m1.
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Over Lesson 4–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 75
B. 72
C. 57
D. 40
Find m2.
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Over Lesson 4–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 75
B. 72
C. 57
D. 40
Find m3.
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Over Lesson 4–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 18
B. 28
C. 50
D. 75
Find m4.
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Over Lesson 4–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 70
B. 90
C. 122
D. 140
Find m5.
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Over Lesson 4–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 35
B. 40
C. 50
D. 100
One angle in an isosceles triangle has a measure of 80°. What is the measure of one of the other two angles?
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You identified and used congruent angles. (Lesson 1–4)
• Name and use corresponding parts of congruent polygons.
• Prove triangles congruent using the definition of congruence.
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• congruent
• congruent polygons
• corresponding parts
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Identify Corresponding Congruent Parts
Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.
Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ.
Sides:
Angles:
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
The support beams on the fence form congruent triangles. In the figure ΔABC ΔDEF, which of the following congruence statements directly matches corresponding angles or sides?
A.
B.
C.
D.
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Use Corresponding Parts of Congruent Triangles
O P CPCTC
mO = mP Definition of congruence
6y – 14 = 40 Substitution
In the diagram, ΔITP ΔNGO. Find the values of x and y.
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Use Corresponding Parts of Congruent Triangles
6y = 54 Add 14 to each side.
y = 9 Divide each side by 6.
NG = IT Definition of congruence
x – 2y = 7.5 Substitution
x – 2(9) = 7.5 y = 9
x – 18 = 7.5 Simplify.
x = 25.5 Add 18 to each side.
CPCTC
Answer: x = 25.5, y = 9
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
In the diagram, ΔFHJ ΔHFG. Find the values of x and y.
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Use the Third Angles Theorem
ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If J K and mJ = 72, find mJIH.
mKJI + mIKJ + mJIK = 180 Triangle Angle-SumTheorem
H K, I I and J J CPCTC
ΔJIK ΔJIH Congruent Triangles
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Use the Third Angles Theorem
144 + mJIK = 180 Simplify.
mJIK = 36 Subtract 144 fromeach side.
Answer: mJIH = 36
72 + 72 + mJIK = 180 Substitution
mJIH = 36 Third Angles Theorem
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 85
B. 45
C. 47.5
D. 95
TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM ΔNJL, KLM KML and mKML = 47.5, find mLNJ.
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Prove That Two Triangles are Congruent
Write a two-column proof.
Prove: ΔLMN ΔPON
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Prove That Two Triangles are Congruent
2. LNM PNO 2. Vertical Angles Theorem
Proof:
Statements Reasons
3. M O
3. Third Angles Theorem
4. ΔLMN ΔPON
4. CPCTC
1. Given1.
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Find the missing information in the following proof.
Prove: ΔQNP ΔOPN
Proof:ReasonsStatements
3. Q O, NPQ PNO 3. Given
5. Definition of Congruent Polygons5. ΔQNP ΔOPN
4. _________________4. QNP ONP ?
2. 2. Reflexive Property ofCongruence
1. 1. Given
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A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. CPCTC
B. Vertical Angles Theorem
C. Third Angle Theorem
D. Definition of Congruent Angles