4-3 Triangle Congruence by ASA and AAS

Learning Target: I can prove triangles congruent using the ASA and AAS Postulate.

Angle-Side-Angle Postulate (ASA Postulate)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.

What can you conclude about the two triangles using ASA Postulate?

A

B

C

D

E

F

Triangle ABC is congruent to Triangle DEF

C

T A

O

D

C

N

I

F

Which two triangles are congruent by ASA?

CAT and CDO

Angle-Angle-Side Theorem (AAS Theorem)If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

What can you conclude about the two triangles using the AAS thm.?

A

B

C D

E

F

Triangle ABC is congruent to Triangle DEF

Given: <S≅<Q, RP bisects <SRQ

P

S

R

QStatementsReasons<S≅<Q GivenRP bisects <SRQ Given<SRP≅<QRP Definition

of bisectRP≅PRSymmetric

PropertyTriangle SPR is AAScongruent to Triangle QPR

Prove: Triangle SPR is congruent to Triangle QPR

Decide whether the triangles are congruent. If so, tell which Theorem you would use. If not, tell what information is needed.

B

E

C

D

FS

T

V

UZ

C

A

B

G

K

H

L

K

G

J

H

1. AAS2. ASA3. N/A4. N/A5. SAS

Given: <K≅<M, KL≅MLProve: Triangle JKL ≅ Triangle PML

M

J

L

K

P

Statements Reasons

<K≅<M Given

KL≅ML Given<MLP≅<KLP Vertical anglesTriangle JKL is ASAcongruent to Triangle PML