Download Triangle Congruence

T RIANGLE C ONGRUENCE
Geometry Honors
Exploration
Postulate
Side-Side-Side (SSS) Postulate – If
three sides of one triangle are
congruent to three sides of
another triangle, then the two
triangles are congruent.
R
T
P
A
N
RAT  PEN
E
Postulate
Side-Angle-Side (SAS) Postulate – If
two sides and the included angle of
one triangle are congruent to two
sides and the included angle of
another triangle, then the two
triangles are congruent.
D
O
C
G
A
DOG  CAT
T
Starting a Proof
Which postulate, if any, could you
use to prove that the two triangles
are congruent?
Q
SSS
Write a valid
P
congruence Z
statement.
ZQPZWP
W
Starting a Proof
Which postulate, if any, could you
use to prove that the two triangles
are congruent?
R
U
K
T
Not congruent
C
Starting a Proof
Which postulate, if any, could you
use to prove that the two triangles
are congruent?
P
SAS
Write a valid
N
L
congruence
A
statement.
PANAPL
Starting a Proof
Which postulate, if any, could you
use to prove that the two triangles
are congruent?
SSS or SAS
H
Write a valid
E
F
congruence
G
I F is the midpoint of HI.
statement.
EFIGFH
Starting a Proof
What other information, if any, do
you need to prove the 2 triangles
are congruent by SSS or SAS?
D
A
B
E
C
Starting a Proof
What other information, if any, do
you need to prove the 2 triangles
are congruent by SSS or SAS?
M
L
D
N
F
E
Starting a Proof
What other information, if any, do
you need to prove the 2 triangles
are congruent by SSS or SAS?
A
M
N
T
U
P
A
Given: X is the
midpoint of AG
N
and of NR.
Prove: ANX  GRX
Statements
X
Reasons
R
G
1. AXN  GXR
1. Vertical Angle Theorem
2. X is the midpoint of AG
3. AX  XG
4. X is the midpoint of NR
5. NX  XR
6. ANX GRX
2. Given
3. Def. of midpoint
4. Given
5. Def. of midpoint
6. SAS Postulate
H OMEWORK
Ways to Prove Triangles
Congruent Worksheet
Ways to Prove Triangles
Congruent #2 Worksheet
Exploration
Postulate
Angle–Side-Angle (ASA) Postulate – 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.
B
A
BIG  ART
I
GR
T
Which two triangles are
congruent?
E
G
P
U
A
T
B
D
N
Write a
valid
congruence
statement.
Theorem
Angle-Angle-Side (AAS) Theorem – If two
angles and a non-included side of one
triangle are congruent to two angles and
a non-included side of another triangle,
then the two triangles are congruent.
B
O
M
A
BOY  MAD
Y
D
Given: XQ TR,
XR bisects QT
Prove: XMQ  RMT
Statements
Q
X
M
R
T
Reasons
1. XQ TR
1. Given
2. X  R
3. XMQ  RMT
4. XR bisects QT
5. QM  TM
6. XMQ RMT
2. Alt. Int. ’s Theorem
3. Vertical Angle Theorem
4. Given
5. Def. of bisect
6. AAS Theorem
Let’s do the
Conclusion Worksheet
together.
H OMEWORK
Conclusions Worksheet #2