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Triangle Congruence. 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. RAT PEN. P. A. E. T. N. Postulate. - PowerPoint PPT Presentation
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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
P
EN
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
C
TA
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
T
Not 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
EFIGFH
I
E
G
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
A
E
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
TP
Given: X is the midpoint of AG and of NR.
Prove: ANX GRX
Statements Reasons
NX
A
R
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
P
E
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.B
O
MA
Y
BOY MAD
D
Given: XQ TR, XR bisects QT
Prove: XMQ RMT
Statements Reasons1. XQ TR 1. Given
2. 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
XQ
T
Let’s do the Conclusion Worksheet
together.
HOMEWORK
Conclusions Worksheet #2
