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Proving Triangles Congruent

Free powerpoints at http//www.worldofteaching.com

The Idea of a Congruence

Two geometric figures with exactly the same

size and shape.

How much do you need to know. . .

. . . about two triangles to

prove that they are congruent?

Corresponding Parts

In Lesson 4.2, you learned that if all six pairs

of corresponding parts (sides and angles) are

congruent, then the triangles are congruent.

?ABC ? ? DEF

Do you need all six ?

NO !

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

B

E

F

A

C

D

- AB ? DE
- ?A ? ? D
- AC ? DF

?ABC ? ? DEF

included angle

Included Angle

The angle between two sides

? H

? G

? I

Included Angle

Name the included angle YE and ES ES and

YS YS and YE

? E

? S

? Y

Angle-Side-Angle (ASA)

B

E

F

A

C

D

- ?A ? ? D
- AB ? DE
- ? B ? ? E

?ABC ? ? DEF

included side

Included Side

The side between two angles

GI

GH

HI

Included Side

Name the included angle ?Y and ?E ?E and

?S ?S and ?Y

YE

ES

SY

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

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

HW Name That Postulate

(when possible)

HW Name That Postulate

(when possible)

Lets Practice

Indicate the additional information needed to

enable us to apply the specified congruence

postulate.

For ASA

?B ? ?D

For SAS

?A ? ?F

For AAS

HW

Indicate the additional information needed to

enable us to apply the specified congruence

postulate.

For ASA

For SAS

For AAS

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