Download 4.2 Triangle Congruence by SSS and SAS

Week
10 day 2
Terrence designed a patio based on the diagram. If AB║DC
and the measure of / ADE = 108°, what is the measure of /BAD
in degrees?
A
B
•
E
D
C
Get out your homework from last night!!!
6
4.3
Triangle
Congruence by
ASA and AAS
You will construct
and justify statement
about triangles using
Angle Side Angle and
Angle Angle Side
Pardekooper
Quick review of yesterday
Side Side Side (SSS) Postulate
If three sides of a triangle are
congruent to three sides of
another triangle, then the
triangles are congruent.
ABCDEF
B
E
A
D
C F
Pardekooper
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
Lets look at some postulates
Angle Side Angle (ASA)
Postulate
If two angles and the included
side of a triangle are congruent
to two angles and the included
side of another triangle, then
the two triangles are
congruent.
B
E
ABCDEF
A
D
C
F
Pardekooper
Just one more postulate
Angle Angle Side (AAS)
Postulate
If two angles and a nonincluded
side of a triangle are congruent
to two angles and a
nonincluded side of another
triangle, then the two triangles
are congruent.
B
ABCDEF
E
A
D
Pardekooper
C
Are the following congruent ?
Yes
Yes
Yes
No
ASA
SAS
AAS
Pardekooper
Now, its time for a proof.
Given: XQTR, XR bisects QT
Prove: XMQRMT
X
Q
M
T
R
Statement
Reason
1. XQTR, XR bisects QT
1. Given
2. TMQM
2. Def. of bisects
3. XMQRMT
3. Vertical ’s are 
4. XQMRTM
4. Alternate interior ’s are 
5. XMQRMT
5. ASA
Pardekooper
Which two are congruent and
why ?
P
W
X
Y
R
Q
ASA
S
T
U
RPQUTS
Pardekooper
Homework