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Over Lesson 4–2
Find m1.
A. 115
B. 105
C. 75
D. 65
Over Lesson 4–2
Find m2.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m3.
A. 75
B. 72
C. 57
D. 40
Over Lesson 4–2
Find m4.
A. 18
B. 28
C. 50
D. 75
Over Lesson 4–2
Find m5.
A. 70
B. 90
C. 122
D. 140
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
B. 40
C. 50
D. 100
You identified and used congruent angles.
• 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 correctly
identifies corresponding angles or sides?
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
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
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 IJK  IKJ
and mIJK = 72, find mJIH.
ΔJIK  ΔJIH Congruent Triangles
mIJK + mIKJ + mJIK = 180 Triangle Angle-Sum
Theorem
Use the Third Angles Theorem
mIJK + mIJK + mJIK = 180
Substitution
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
D. 95
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  OPN
?
1.
2.
5. ΔQNP  ΔOPN
5. Definition of Congruent Polygons
A. CPCTC
B. Vertical Angles Theorem
C. Third Angles Theorem
D. Definition of Congruent
Angles