geometry 5-6 asa and aas

5-6ASA & AAS

Proving Triangles Congruent

jc-schools.net/PPT/geometrycongruence.ppt

Angle-Side-Angle (ASA) Congruence Postulate

Two angles and the INCLUDED side

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 (ASA)

1. A D2. AB DE

3. B E

ABC DEF

B

A

C

E

D

F

included side

jc-schools.net/PPT/geometrycongruence.ppt

Before we start…let’s get a few things straight

INCLUDED SIDE

A B

C

X Z

Y

The side between two angles

Included Side

GI HI GH

Name the included side:

Y and E

E and S

S and Y

Included Side

SY

E

YE

ES

SY

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

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)

1. A D

2. B E

3. BC EF

ABC DEF

B

A

C

E

D

F

Non-included side

jc-schools.net/PPT/geometrycongruence.ppt

Warning: 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: 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

}Your Only Ways To Prove

Triangles Are Congruent

Name That Postulate(when possible)

ASAAAA

SSA

jc-schools.net/PPT/geometrycongruence.ppt

Overlapping sides are congruent in

each triangle by the REFLEXIVE property

Vertical Angles

are congruen

t

Alt Int Angles are congruent

given parallel

lines

Things you can mark on a triangle when they aren’t marked.

Ex 1

statement. congruence a Write.

and ,, and In

LE

NLDENDΔLMNΔDEF

DEF NLM

Ex 2

What other pair of angles needs to be marked so that the two triangles are congruent by AAS?

F

D

E

M

L

N

NE

Ex 3

What other pair of angles needs to be marked so that the two triangles are congruent by ASA?

F

D

E

M

L

N

LD

Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible.

ΔGIH ΔJIK by AAS

G

I

H J

KEx 4

ΔABC ΔEDC by ASA

B A

C

ED

Ex 5

Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible.

ΔJMK ΔLKM by SAS or ASA

J K

LM

Ex 7

Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible.

Not possible

K

J

L

T

U

Ex 8

Determine if whether each pair of triangles is congruent by ASA or AAS. If it is not possible to prove that they are congruent, write not possible.

V