Proving Triangles Congruent

Proving Triangles Congruent

jc-schools.net/PPT/geometrycongruence.ppt

Angle-Side-Angle (ASA)Angle-Side-Angle (ASA)

Postulate 8-3: 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.

Angle-Side-Angle-Side-AngleAngle (ASA) (ASA)

1. A D

2. AB DE

3. B E

ABC DEF

B

A

C

E

D

F

included side

jc-schools.net/PPT/geometrycongruence.ppt

Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)

Theorem 8-1: If two angles and the

nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangle, then the two triangles are congruent.

Angle-Angle-Side (AAS)Angle-Angle-Side (AAS)

1. A D

2. B E

3. BC EF

ABC DEF

B

A

C

E

D

F

Non-included

sidejc-schools.net/PPT/geometrycongruence.ppt

Warning:Warning: No SSA Postulate No SSA Postulate

A C

B

D

E

F

NOT CONGRUENT

There is no such thing as an SSA

postulate!

jc-schools.net/PPT/geometrycongruence.ppt

Warning:Warning: No AAA Postulate No AAA Postulate

A C

B

D

E

F

There is no such thing as an AAA

postulate!

NOT CONGRUENTjc-schools.net/PPT/geometrycongruence.ppt

The Congruence PostulatesThe Congruence Postulates

SSS correspondence

ASA correspondence

SAS correspondence

AAS correspondence

SSA correspondence

AAA correspondence

jc-schools.net/PPT/geometrycongruence.ppt

Name That PostulateName That Postulate

SASSASASAASA

SSSSSSSSASSA

(when possible)

jc-schools.net/PPT/geometrycongruence.ppt

Name That PostulateName That Postulate(when possible)

ASAASA

SASASS

AAAAAA

SSASSA

jc-schools.net/PPT/geometrycongruence.ppt

Let’s PracticeLet’s PracticeIndicate the additional information needed to enable us to apply the specified congruence postulate.

For ASA:

For SAS:

B D

For AAS: A F

AC FE

jc-schools.net/PPT/geometrycongruence.ppt

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

For ASA:

For SAS:

For AAS:

jc-schools.net/PPT/geometrycongruence.ppt

HomeworkWork Packet: ASA and AAS