Today you will
Name and use corresponding parts of congruent polygons
Prove triangles are congruent using the definition of
congruence.
4.3 Congruent Triangles
Definition of Congruent Polygons:
Two polygons are congruent IFF
their corresponding parts are congruent.
List all pairs of corresponding parts.
CAT =
DOG
Write a congruence statement and identify all pairs of
corresponding congruent parts.
H
Y
X
Z
K
J
Since definitions are biconditionals, if two triangles are
then we know all corresponding parts are
.
,
So we say,
"Corresponding Parts of Congruent Triangles are Congruent"
or CPCTC
A
J
9
H
5y-12
113
C
4x-3
B
ABC
x = _______
K
KJH
y = ________
Are the triangles congruent?
D
A
C
B
E
Third Angles Theorem:
If 2 angles of one triangle are
angles of a second triangle,
to two
then the third angles of the triangles are
((
(
((
(
Properties of Triangle Conguence:
Reflexive Property of Triangle Congruence:
ABC
ABC
Symmetric Property of Triangle Congruence:
If
EFG then
ABC
EFG
Transitive Property of Triangle Congruence:
If
ABC
EFG and
then
ABC
EFG
JKL
JKL
ABC
N
M
Given: MN
MN
QP
QP
O
O is the midpt. of MQ and PN
Prove:
MNO
QPO
P
Statements
Q
Reasons