Identify Corresponding Congruent Parts
Show that polygons ABCDE
and RTPSQ 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.
B.
C.
D.
A.
B.
C.
D.
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
A.
B.
C.
D.
A
B
C
D
You will prove this!
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.
GIVEN: ΔJIK  ΔJIH
Use the 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
Find the missing information in the following proof.
Prove: ΔQNP  ΔOPN
Proof:
Statements
1.
Q  O, NPQ  PNO
Reasons
1. Given