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Triangle Congruence - PowerPoint PPT Presentation

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.

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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

ZQPZWP

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

PANAPL

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.

EFIGFH

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

• 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

E

G

P

N

U

A

T

Write a valid congruence statement.

B

D

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

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.

• Conclusions Worksheet #2