Notes 4.1-4.3 Triangle Congruence

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# Notes 4.1-4.3 Triangle Congruence - PowerPoint PPT Presentation

Notes 4.1-4.3 Triangle Congruence Learning Targets I can recognize congruent figures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS. Congruence.

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Learning TargetsI can recognize congruentfigures and their corresponding parts. I can prove triangles congruent using SSS and SAS. I can prove triangles congruent using ASA and AAS.

Congruence

Two geometric figures with exactly the same size and shape.

Corresponding Parts

B

A

C

E

F

D

If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent.

Example 1

• AB DE
• BC EF
• AC DF
•  A  D
•  B  E
•  C  F

ABC DEF

SSS

SAS

ASA

AAS

Do you need all six ?

NO !

Side-Side-Side (SSS)

B

A

C

E

F

• Example 1
• AB DE
• BC EF
• AC DF

D

ABC DEF

Included Angle

The angle between two sides

H

G

I

Side-Angle-Side (SAS)

B

E

F

A

C

D

• AB DE
• A D
• AC DF

ABC DEF

included

angle

Included Side

The side between two angles

GI

GH

HI

E

Y

S

Included Side

Name the included side:

Y and E

E and S

S and Y

YE

ES

SY

Angle-Side-Angle (ASA)

B

E

F

A

C

D

• A D
• AB  DE
• B E

ABC DEF

included

side

Angle-Angle-Side (AAS)

B

E

F

A

C

D

• A D
• B E
• BC  EF

ABC DEF

Non-included

side

Warning: No SSA Postulate

There is no such thing as an SSA postulate!

E

B

F

A

C

D

NOT CONGRUENT

Warning: No AAA Postulate

There is no such thing as an AAA postulate!

E

B

A

C

F

D

NOT CONGRUENT

SSS

• ASA
• SAS
• AAS
• SSA
• AAA

The Congruence Postulates

Name That Postulate

(when possible)

SAS

ASA

SSA

SSS

Name That Postulate

(when possible)

AAA

ASA

SSA

SAS

Name That Postulate

(when possible)

Vertical Angles

Reflexive Property

SAS

SAS

Reflexive Property

Vertical Angles

SSA

SAS

Let’s Practice

ACFE

Indicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

B D

For SAS:

AF

For AAS: