Triangle Congruence (SSS and SAS)
section 4-5
In Lesson 4-3, you proved triangles congruent by showing that all six pairs of
corresponding parts were congruent.
The property of triangle rigidity gives you a shortcut for proving that two
triangles are congruent. It states that if the side lengths of a triangle are given,
the triangle can have only one possible shape. For example, you only need to
know that a pair of triangles has 3 pairs of congruent sides in order to be certain
that the triangles are congruent. This is expressed in our next postulate.
**Real-life application of the SSS postulate - the triangle is the strongest possible
shape for construction
* See the attachments for a 2 minute video on triangles used in construction. *
problem # 1 - Explain why
PQR
Q
PSR.
R
P
S
An included angle is an angle formed by two
adjacent sides of a polygon.
B is the
included angle between sides AB and BC.
It can also be shown that only two pairs of congruent corresponding sides are needed
to prove the congruence of two triangles, if the included angles are also congruent.
problem # 2 - The figure to the right is a model
of the Statue of Liberty, showing
part of its support structure. Use
the SAS postulate to explain why
KPN
LPM.
M
K
P
N
L
The SAS Postulate guarantees that if you are given the lengths of two sides and
the measure of the included angle, you can construct one and only one triangle.
problem # 3 - Show that the triangles in each pair below are congruent.
X
U
a. If x = 3, show that
UVW
YXZ
2
4
3x - 5
x
W
3
V
x-1
Y
D
b. If y = 7, show that
DEF
Z
F
15
126
JGH
24
E
G
2y + 1
(12y + 42)
y 2 - 4y + 3
J
H
problem # 4 - Prove the triangles are congruent.
m; EG
HF
Prove:
EGF
HFG
1. l
2.
m; EG
EGF
3. FG
4.
G
E
Given: l
HF
1.
HFG
2.
3.
GF
EGF
F
HFG
4.
l
H
m