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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
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