4.5 – Prove Triangles Congruent by ASA and AAS

Geometry Ms. Rinaldi

Angle-Side-Angle (ASA) Congruence Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

If Angle

Side

Angle

Then TC

A

B

C

R

S

T

TRCA

RSTABC

RA

EXAMPLE 1 Use ASA

Decide whether the congruence statement is true. Explain your reasoning.

JKLABC

SOLUTION

KJBAJA

KB (A)

(S)

(A)

So, by ASA, JKLABC

EXAMPLE 2 Use ASA

Decide whether the congruence statement is true. Explain your reasoning.

PONLMN

Angle-Angle-Side (AAS) Congruence Postulate

If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of a second triangle, then the two triangles are congruent.

If Angle

Angle

Side

Then

TC

A

B

C

R

S

T

STBC RSTABC

RA

EXAMPLE 3 Use AAS

Decide whether the congruence statement is true. Explain your reasoning.

TURRST

SOLUTION

RTRT

STRURT SU (A)

(A)

(S)

So, by AAS, TURRST

EXAMPLE 4 Use AAS

Decide whether the congruence statement is true. Explain your reasoning.

FGEHDE

EXAMPLE 5 Use ASA or AAS

State the third congruence that must be given to prove that using the indicated postulate.DEFABC

A

B

C

D

E

F

Given:

Use the ASA Congruence Postulate.

DEAB DA

EXAMPLE 6 Use ASA or AAS

State the third congruence that must be given to prove that using the indicated postulate.DEFABC

A

B

C

D

E

F

Given:

Use the ASA Congruence Postulate.

EB FC

EXAMPLE 7 Use ASA or AAS

State the third congruence that must be given to prove that using the indicated postulate.DEFABC

A

B

C

D

E

F

Given:

Use the AAS Congruence Postulate.

FC DA