geometry honors t riangle c ongruence. exploration

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