4-4 & 4-5: tests for congruent triangles objective: use sss, sas, asa & aas to prove...
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4-4 & 4-5: Tests for Congruent Triangles
Objective: Use SSS, SAS, ASA & AAS to prove triangle congruence.
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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
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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
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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
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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
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Homework:
WS 4-4 #1-10
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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
![Page 8: 4-4 & 4-5: Tests for Congruent Triangles Objective: Use SSS, SAS, ASA & AAS to prove triangle congruence](https://reader033.vdocuments.mx/reader033/viewer/2022051113/56649cee5503460f949bc524/html5/thumbnails/8.jpg)
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
![Page 9: 4-4 & 4-5: Tests for Congruent Triangles Objective: Use SSS, SAS, ASA & AAS to prove triangle congruence](https://reader033.vdocuments.mx/reader033/viewer/2022051113/56649cee5503460f949bc524/html5/thumbnails/9.jpg)
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
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Homework:
WS 4-4 & 4-5#1-12
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Ex. 1:
Given: A is the midpoint of HT
A is the midpoint of RS
Prove: ART ASHH
S
A
R
T
Statements Reasons
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Ex. 2:
Given: CK bisects OCE
CK bisects OKE
Prove: OCK ECK
Statements ReasonsE
K
O
C
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D C
BA
Ex. 3:
Given: AB CD
AD BC
Prove: A C
Statements Reasons
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Ex. 4:
Given: CK bisects OCE
O E
Prove: OK EK
Statements ReasonsE
K
O
C
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Homework:
WS Proofs #2