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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
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.
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.
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.
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.
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.
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?
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.
• congruent
• congruent polygons
• corresponding parts
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:
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.
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.
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
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.
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
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
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.
Prove That Two Triangles are Congruent
Write a two-column proof.
Prove: ΔLMN ΔPON
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.
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
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
