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## PowerPoint Slideshow about ' Triangle Congruence' - katelyn-hogan

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### Triangle Congruence

Geometry Honors

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

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

DOG CAT

C

G

T

O

A

Which postulate, if any, could you use to prove that the two triangles are congruent?

Q

SSS

Write a valid congruence statement.

P

Z

ZQPZWP

W

Which postulate, if any, could you use to prove that the two triangles are congruent?

R

K

U

T

C

Not congruent

Which postulate, if any, could you use to prove that the two triangles are congruent?

P

SAS

Write a valid congruence statement.

N

L

A

PANAPL

Which postulate, if any, could you use to prove that the two triangles are congruent?

SSS or SAS

H

Write a valid congruence statement.

E

F

G

I

F is the midpoint of HI.

EFIGFH

What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS?

D

A

B

E

C

What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS?

M

D

L

N

E

F

What other information, if any, do you need to prove the 2 triangles are congruent by SSS or SAS?

A

N

M

P

T

U

Given: X is the midpoint of AG and of NR.

R

X

N

Prove: ANX GRX

G

1. Vertical Angle Theorem

1. AXN GXR

2. Given

2. X is the midpoint of AG

3. AX XG

3. Def. of midpoint

4. Given

4. X is the midpoint of NR

5. Def. of midpoint

5. NX XR

6. SAS Postulate

6. ANX GRX

Homework

- Ways to Prove Triangles Congruent Worksheet
- Ways to Prove Triangles Congruent #2 Worksheet

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

R

T

G

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.

M

B

A

BOY MAD

O

D

Y

Given: XQ TR, XR bisects QT

X

M

R

Prove: XMQ RMT

T

1. Given

1. XQ TR

2. Alt. Int. ’s Theorem

2. X R

3. XMQ RMT

3. Vertical Angle Theorem

4. Given

4. XR bisects QT

5. Def. of bisect

5. QM TM

6. AAS Theorem

6. XMQ RMT

Let’s do the Conclusion Worksheet together.

Homework

- Conclusions Worksheet #2

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