techmathi - 4.3 - using congruent triangles

Bell RingerBell Ringer

Angle – Side – Angle Postulate - If two angles and the included side of one

triangle are congruent to the corresponding parts of another triangle, then the 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

The side between two angles

Included SideIncluded Side

GI HI GH

Name the included side:

Y and E

E and S

S and Y

Included SideIncluded Side

SY

E

YE

ES

SY

Angle – Angle – Angle Postulate

- If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the 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

side

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!

Warning:Warning: No AAA Postulate No AAA Postulate

A C

B

D

E

F

There is no such thing as an AAA

postulate!

NOT CONGRUENT

Name That PostulateName That Postulate

SASSASASAASA

SSSSSSSSASSA

(when possible)

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

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

For ASA:

For SAS:

For AAS: