Download Prove that triangles are congruent using SSS and

Warm Up
Name all the things that can you conclude from each
diagram?.
1. 2 things
2. 3 things
3.
4 things
4.2: Proving Triangles are Congruent
by SSS and SAS
Objectives:
 Prove that triangles are congruent using
SSS and SAS Congruence Postulates.
 Use congruence postulates in real-life
problems.
How much information do
you need to know to tell
whether two triangles are
congruent?
Ways to Prove 2 Triangles Congruent
1. All sides and All angles are congruent
2. SSS
3. SAS
Postulate 4-1: Side-Side-Side (SSS)
Congruence Postulate
If three sides of one triangle are congruent to
three sides of a second triangle, then the two
triangles are congruent.
Checkpoint?

Is there enough information given to prove
that the two triangles are congruent?
Explain.
M
L
P
N
Triangle Congruence by SSS
Given: M is the midpoint of XY, AX
Prove: AMX
AMY
AY
Write a paragraph proof.
Copy the diagram. Mark the congruent sides.
You are given that M is the midpoint of XY, and AX AY.
Midpoint M implies MX MY. AM AM by the Reflexive
Property of Congruence, so AMX
AMY by the SSS
Postulate.
Postulate 4-2: Side-Angle-Side (SAS)
Congruence Postulate
If two sides and the
included angle of one
triangle are congruent
to two sides and the
included angle of
second triangle, then
the two triangles are
congruent.
Given :
C is the midpoint of AD and of BE
Prove: Triangle ABC = DEC
Given: RSG RSH, SG SH
From the information given, can you prove
RSG
RSH? Explain.
Copy the diagram. Mark what is given on the diagram.
It is given that RSG RSH and SG SH.
RS RS by the Reflexive Property of Congruence.
Two pairs of corresponding sides and their included angles
are congruent, so RSG
RSH by the SAS Postulate.
HW Assignment
Section 4.2
Pages 189-191
#1-11, 14-21, 23-27