20
TRIANGLE CONGRUENCE
TRIANGLE CONGRUENCE
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
TA
PE
N
RAT PEN
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.
DOG CATD
OG
CT
A
Which postulate, if any, could you use to prove that the two triangles are congruent?
Starting a Proof
W
Z
Q
PWrite a valid congruence statement.
SSS
ZQPZWP
Which postulate, if any, could you use to prove that the two triangles are congruent?
Starting a Proof
TNot congruent
RU
C
K
Which postulate, if any, could you use to prove that the two triangles are congruent?
Starting a Proof
P
Write a valid congruence statement.
SAS
PANAPL
L
A
N
Which postulate, if any, could you use to prove that the two triangles are congruent?
Starting a Proof
FWrite a valid congruence statement.
SSS or SAS
EFIGFHI
EG
H
F is the midpoint of HI.
What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS?
Starting a Proof
B
C
AE
D
What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS?
Starting a Proof
N
M
L
D
EF
What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS?
Starting a Proof
M
A
N
U
T P
Given: X is the midpoint of AG and of NR.
Prove: ANX GRXStatements Reasons
NX
AR
1. AXN GXR 1. Vertical Angle Theorem2. X is the midpoint of
AG2. Given
3. AX XG 3. Def. of midpoint4. X is the midpoint of NR
4. Given
6. ANX GRX 6. SAS Postulate
G
5. NX XR 5. Def. of midpoint
HOMEWORK
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
I
A
RG
BIG ART
T
Which two triangles are congruent?
G
AT
PE
N
B
U
D
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.BO
MA
Y
BOY MAD
D
Given: XQ TR, XR bisects QT
Prove: XMQ RMTStatements Reasons
1. XQ TR 1. Given2. X R 2. Alt. Int. ’s
Theorem3. XMQ RMT 3. Vertical Angle Theorem4. XR bisects QT 4. Given
6. XMQ RMT 6. AAS Theorem5. QM TM 5. Def. of bisect
RM
X Q
T
Let’s do the Conclusion Worksheet
together.
HOMEWORK
Conclusions Worksheet #2
