4-3 Congruent Triangles
4-3 Congruent Triangles
4-3 Congruent Triangles
A
D
F
E
C
B
Corresponding sides and angles
C T
A B R S
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:
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 CPCTC
mO = mP Definition of congruence
6y – 14 = 40 Substitution
6y = 54 Add 14 to each side.
y= 9 Divide each side by 6.
CPCTC
NG = IT 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 mIJK = 72, find
mJIH.
ΔJIK ΔJIH Congruent Triangles
mIJK + mIKJ + mJIK = 180 Triangle Angle-Sum Theorem
mIJK + mIJK + mJIK = 180 Substitution
72 + 72 + mJIK = 180 Substitution
144 + mJIK = 180 Simplify.
mJIK = 36 Subtract 144 from each side.
mJIH = 36 Third Angles Theorem
Answer: mJIH = 36
Write a two-column proof.
1. 1. Given
Statements Reasons
1. 1. Given
2. 2. Reflexive Property of
Congruence
3. Q O, NPQ PNO 3. Given
4. QNP ONP Third angle theorem
4. _________________
?
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