Download 4.2 Triangle Congruence by SSS and SAS

4.2
Triangle
Congruence by
SSS and SAS
You will construct
and justify
statements about
triangles using
Side Side Side
and Side Angle
Side
Pardekooper
First, we need to look
at some things.
 What makes two items
congruent?
 All the corresponding
sides are congruent.
 All the corresponding
angles are congruent.
Pardekooper
Lets label the
congruent parts
L
P
N
M Q
R
N R
NL  RP
L P
LM PQ
M Q
NM RQ
NLM  RPQ
Pardekooper
There is a theorem.
If two angles of one triangle
are congruent to two
angles of another triangle,
then the third angle is
congruent
Pardekooper
Lets look at some postulates
Side Side Side (SSS) Postulate
If three sides of a triangle are
congruent to three sides of
another triangle, then the
triangles are congruent.
B
ABCDEF
E
A
D
C F
Pardekooper
Just one more postulate
Side Angle Side (SAS) Postulate
If two sides and the included angle of a
triangle are congruent to two sides
and the included angle of another
triangle, then the triangles are
congruent.
ABCDEF
B
E
A
Pardekooper
D
C F
Are the following congruent ?
No
Yes
It’s the
wrong
SAS
SSS
angle
Pardekooper
One
angle is
off
Now, its time for a proof.
Given: HFHJ, FGJI, H is midpoint of GI.
Prove: FGHJIH
F
G
J
H
I
Statement
Reason
1. HFHJ, FGJI
1. Given
H is midpont of GI
2. GHHI
2. Def. of midpoint
3. FGHJIH
3. SSS
Pardekooper
Last proof.
Given: EBCB, ABDB
Prove: AEBDCB
E
D
C
B
A
Statement
Reason
1. EBCB, ABDB
1. Given
2. EBACBD
2. Vertical ’s
3. AEBDCB
3. SAS
Pardekooper