4.6: Use Congruent Triangles
Properties of Congruent Triangles
ABC  DEF
A
B
D
C
E
What pairs of angles and sides are congruent?
F
Using CPCTC:
• Once you know that triangles are congruent, you can
make conclusions about corresponding sides and
angles because Corresponding Parts of Congruent
Triangles are Congruent (CPCTC).
Ex.1: Suppose you know that ABD  CDB by SAS.
Which additional pairs of sides and angles are
congruent by CPCTC?
A
B
D
C
Example 2:
Tell which triangles you can show are congruent in order to
prove the statement. What postulate or theorem would
you use? <ACB
<DCB
A
B
C
D
Example 3:
Tell which triangles you can show are congruent in order to
prove the statement. What postulate or theorem would
you use? <PLM
<PNO
M
N
P
L
O
Example 4:
Tell which triangles you can show are congruent in order to
prove the statement. What postulate or theorem would
you use? MJ
ML
K
J
M
L
Example 5:
Tell which triangles you can show are congruent in order to
prove the statement. What postulate or theorem would
you use? ML
ON
M
L
N
O
Example 6:
Tell which triangles you can show are congruent in order to
prove the statement. What postulate or theorem would
you use?
BC
DA
B
A
C
D
Example 7
Is enough information given in the figure to show
that the given statement is true?  B C
A
D
E
B
C
Example 8
Is enough information given in the figure to show
that the given statement is true?  A C
D
A
E
C
B
Given: WZ  YZ
and X is the midpoint of WY
Prove: W  Y
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
Y
Z
X
W
Q
Given: QR  SR
and PR bisects SRQ
Prove: PS  PQ
P
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
R
S