Download Lesson 11.2 - Congruent Triangles

Lesson 11.2 - Congruent Triangles
We will develop criteria for proving
triangle congruence
and
I will determine which congruence
criteria can be used to show that two
triangles are congruent.
October 31, 2016
There are five combinations of three
congruent parts that suggest that two
triangles are identical. List the five different
combinations that seem to guarantee that two
triangles are congruent. These combinations
are called congruent triangle methods.
SSS
SAS
ASA
AAS
HL
SSS - Side-Side-Side Congruence Postulate:
If 3 sides of one triangle are congruent to 3
sides of another, then the 2 triangles are
congruent.
B
A
A
C
P
M
Congruence Statement - ΔABC  ΔMAP
SAS - Side-Angle-Side Congruence Postulate:
If 2 sides and the included angle of one
triangle are congruent to 2 sides and the
included angle of another, then the 2 triangles
are congruent.
B
A
U
C
N
F
Congruency Statement - ΔABC  ΔFUN
ASA - Angle-Side-Angle Congruence
Postulate:
If 2 angles and the included side of one
triangle are congruent to 2 angles and the
included side of another, then the 2 triangles
are congruent.
B
A
Y
C
X
Z
Congruency Statement - ΔABC  ΔZYX
AAS - Angle-Angle-Side Congruence
Theorem:
If 2 angles and a non-included side of one
triangle are congruent to 2 angles and a nonincluded side of another, then the 2 triangles
are congruent.
B
A
Y
C
X
Congruency Statement - ΔABC  ΔZYX
Z
Are the triangles congruent? If so, write
the congruence statement and state the
reason (postulate).
1.
U
V
2.
B
Y
Not
enough
info.
SSS
X
W
C
∆UVX  ∆WVX
Z
D
A
3. A
C
A
4.
B
B
N
L
A
D
C
M
B
Hint: Redraw by pulling triangles apart.
Yes.
ABC  MLN
SAS
Yes.
ABC  DCB
SAS
C B
BC  BC
D
C