4-4 & 4-5: Tests for Congruent Triangles

Objective: Use SSS, SAS, ASA & AAS to prove triangle congruence.

SSS Postulate If the sides of one triangle are congruent to the sides of another triangle, then the triangles are congruent.

F

E

DC

B

A

If AB DE, BC EF , and AC DF

then ABC DEF

SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

F

E

DC

B

A

If AB DE, BC EF , and B E

then ABC DEF

Ex. 1: Determine if the triangles can be proved congruent.

If so, state why, and make a congruence statement.

D C

BA

a.

b.

E

BO

L

G

Ex. 1, cnt’d: Determine if the triangles can be proved congruent. If so, state why, and make a congruence

statement. c.

d.

R

IA

T

S

D C

BA

Homework:

WS 4-4 #1-10

ASA Postulate If two angles and the included side of one triangle are congruent two angles and the included side of another triangle, then the triangles are congruent.

F

E

DC

B

A

If A D, B E, and AB DE

then ABC DEF

AAS Postulate If two angles and a non-included side of one triangle are congruent two angles and a non-included side of another triangle, then the triangles are congruent.

F

E

DC

B

A

If A D, B E, and BC EF

then ABC DEF

Ex. 2: Determine if the triangles can be proved congruent.

If so, state why, and make a congruence statement.

a.

b.

G

F

E

D

G

F

E

D

Homework:

WS 4-4 & 4-5#1-12

Ex. 1:

Given: A is the midpoint of HT

A is the midpoint of RS

Prove: ART ASHH

S

A

R

T

Statements Reasons

Ex. 2:

Given: CK bisects OCE

CK bisects OKE

Prove: OCK ECK

Statements ReasonsE

K

O

C

D C

BA

Ex. 3:

Given: AB CD

AD BC

Prove: A C

Statements Reasons

Ex. 4:

Given: CK bisects OCE

O E

Prove: OK EK

Statements ReasonsE

K

O

C

Homework:

WS Proofs #2