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
Find m1.
A. 115
B. 105
C. 75
D. 65
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m2.
A. 75
B. 72
C. 57
D. 40
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m3.
A. 75
B. 72
C. 57
D. 40
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m4.
A. 18
B. 28
C. 50
D. 75
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
Find m5.
A. 70
B. 90
C. 122
D. 140
0%
D
0%
C
0%
B
A
0%
A.
B.
C.
D.
A
B
C
D
Over Lesson 4–2
One angle in an isosceles triangle has a measure of
80°. What is the measure of one of the other two
angles?
A. 35
0%
B
D. 100
A
0%
A
B
C
0%
D
D
C. 50
A.
B.
C.
0%
D.
C
B. 40
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.
Angles:
Sides:
Answer: All corresponding parts of the two polygons
are congruent. Therefore, ABCDE  RTPSQ.
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.
A.
B.
C.
D.
B.
C.
D.
0%
D
0%
C
0%
B
A
0%
A
B
C
D
Use Corresponding Parts of Congruent
Triangles
In the diagram, ΔITP  ΔNGO. Find the values of
x and y.
O  P
mO = mP
6y – 14 = 40
CPCTC
Definition of congruence
Substitution
Use Corresponding Parts of Congruent
Triangles
6y = 54
y= 9
Add 14 to each side.
Divide each side by 6.
CPCTC
NG = IT
x – 2y = 7.5
x – 2(9) = 7.5
x – 18 = 7.5
x = 25.5
Answer: x = 25.5, y = 9
Definition of congruence
Substitution
y=9
Simplify.
Add 18 to each side.
In the diagram, ΔFHJ  ΔHFG. Find the values of
x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
0%
B
A
0%
A
B
C
0%
D
D
D. x = 4.5, y = 5.5
C
C. x = 1.8, y = 19
A.
B.
C.
0%
D.
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 mJ = 72, find mJIH.
ΔJIK  ΔJIH Congruent Triangles
mKJI + mIKJ + mJIK = 180 Triangle Angle-Sum
Theorem
H  K, I  I and J  J
CPCTC
Use the Third Angles Theorem
72 + 72 + mJIK = 180 Substitution
144 + mJIK = 180 Simplify.
mJIK = 36
Subtract 144 from
each side.
mJIH = 36
Third Angles Theorem
Answer: mJIH = 36
TILES A drawing of a tile contains a series of
triangles, rectangles, squares, and a circle.
If ΔKLM  ΔNJL, KLM  KML and mKML = 47.5,
find mLNJ.
A. 85
B. 45
C. 47.5
0%
D
0%
C
0%
B
0%
A
D. 95
A.
B.
C.
D.
A
B
C
D
Prove That Two Triangles are Congruent
Write a two-column proof.
Prove: ΔLMN  ΔPON
Prove That Two Triangles are Congruent
Proof:
Statements
Reasons
1.
1. Given
2. LNM  PNO
2. Vertical Angles Theorem
3. M  O
3. Third Angles Theorem
4. ΔLMN  ΔPON
4. CPCTC
Find the missing information in the following proof.
Prove: ΔQNP  ΔOPN
Proof:
Statements
Reasons
1. Given
2. Reflexive Property of
Congruence
3. Q  O, NPQ  PNO 3. Given
4. _________________
4. QNP  ONP
?
1.
2.
5. ΔQNP  ΔOPN
5. Definition of Congruent Polygons
A. CPCTC
B. Vertical Angles Theorem
C. Third Angle Theorem
A
B
C
0%
D
D
0%
B
A
0%
C
D. Definition of Congruent
Angles
A.
B.
C.
0%
D.