4-3 Congruent Triangles
You identified and used congruent angles.
• Name and use corresponding parts of
congruent polygons.
• Prove triangles congruent using the
definition of congruence.
Vocabulary
• If two geometric figures have exactly the
same shape and size, they are congruent.
• Un two congruent polygons, all of the
parts of one polygon are congruent to the
corresponding parts or matching parts of
the other polygon. These corresponding
parts include corresponding angles and
corresponding sides.
The Right Match
Congruent
Not congruent
A
D
F
C
B

E
Corresponding sides and angles
C
A
T
B
Corresponding Angles
S
R
Corresponding sides
A  R
C  T
AB
RS
B  S
BC
ST
AC
RT
H
B
A
C
K
J
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.
The phrase “if and only if” in the congruent polygon
definition means that both the conditional and its
converse are true. So, if two polygons are
congruent, then their corresponding parts are
congruent. For triangles, Corresponding parts of
congruent triangles are congruent, or CPCTC.
C PCTC
In the diagram, ΔITP 
ΔNGO. Find the values
of x and y.
O  P
mO = mP
6y – 14 = 40
6y = 54
y= 9
NG = IT
CPCTC
Definition of congruence
Substitution
Add 14 to each side.
Divide each side by 6.
CPCTC
Definition of congruence
x – 2y = 7.5
Substitution y = 9
x – 18 = 7.5
x = 25.5, y = 9
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
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
mIJK + mIJK + mJIK = 180 Substitution
72 + 72 + mJIK = 180
144 + mJIK = 180
Substitution
Simplify.
mJIK = 36
Subtract 144 from each side.
mJIH = 36
Third Angles Theorem
Answer: mJIH = 36
Write a two-column proof.
Prove: ΔLMN  ΔPON
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
Statements
Reasons
1. Given
2. Reflexive Property of
Congruence
3. Q  O, NPQ  PNO 3. Given
Third angle
theorem
4. _________________
4. QNP  ONP
?
1.
2.
5. ΔQNP  ΔOPN
5. Definition of Congruent Polygons
Like congruence of segments and angles, congruence of
triangles is reflexive, symmetric, and transitive.
4-3 Assignment
Page 259, 10, 12, 13-16, 18-20