4.2: Triangle Congruency by SSS
and SAS
Objectives:
To prove two triangles congruent using the
SSS and SAS Postulates.
Side-Side-Side (SSS)Postulate
If 3 sides of one triangle are  to 3 sides of another
triangle, then the triangles are  .
ABC  DEF
(Notice the order in which the congruency statement is given)
B
A
D
C
1. Which other side do we know is congruent?
Why?
2. Which two triangles are congruent?
3. How do you know?
Included Angles and Sides
N
B
BX
X
is included between Angle B and Angle X
N is included between NB and NX.
Which side is included between angle N
and angle B?
Which angle is included between BX and
NX?
Side-Angle-Side (SAS) Postulate
If 2 sides and the included angle of one triangle
are  to 2 sides and the included angle of
another triangle, then the 2 triangles are .
ABC  DEF
Again, notice the order of the congruency statement.
Name the triangle congruence postulate, if any, that you can use to prove
each pair of triangles congruent. Then write a congruency statement.
Q
1.
K
P
M
2.
O
N
J
C
M
N
A
3.
L
S R
P
What other information do you need to prove ABC  CDA by
SSS?
7
A
6
8
D
B
C
7
From the information given, can you prove AEB  CDB ? Explain.
D
E
B
A
C
ASA Postulate
Angle-Side-Angle
• If two angles and the included side of one
triangle are congruent to two angles and the
included side of another triangle, then the
two triangles are congruent.
AAS Theorem
Angle-Angle-Side
• If two angles and a nonincluded side of one
triangle are congruent to two angles and the
corresponding nonincluded side of another
triangle, then the triangles are congruent.
Can you prove the triangles are congruent?
HL
Hypotenuse-Leg
If the hypotenuse and a leg of one right triangle are congruent
To the hypotenuse and a leg of another right triangle, then
The triangles are congruent.
Can you prove the triangles are congruent?
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History According to legend,
one of Napoleon’s officers used
congruent triangles to estimate
the width of a river. On the
riverbank, the officer stood up
straight and lowered the visor
of his cap until the farthest thing
he could see was the edge of the
opposite bank. He then turned
and noted the spot on his side
of the river that was in line with
his eye and the tip of his visor.