Download 4.2 Triangle Congruence SSS and SAS

4.2 Triangle Congruence SSS and SAS
D.I.R.T?
1) Given figure DEFG ≅ NSTP, list all the congruent parts.
Find the missing variable.
Given figures MNOW≅ BDCR, fill in the blanks.
10
M
D
N
C
100
O
15
W
R
B
2) BD=_________
3) m<C=__________
4) MW≅________
5) m<M=__________
6) <R≅________
7) OW= ___________
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4.2 Triangle Congruence by SSS and SAS
The word included used frequently when referring to angles and side of a triangle.
Objective: To prove two triangles congruent using the SSS and SAS Postulates
A
(SSS)
Postulate 4­1 Side­Side­Side If three sides on one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Given the two sides, what is the included angle?
AC and AB AC and CB _____________
<B is included by which two sides? _________
Q
H
Given the two angles, what is the included side?
<A and <B ______________
G
F
P
R
C
B
<B and <C _____________
AC is the included side for which two angles? ______________
~
GHF = PQR
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4.2 Triangle Congruence SSS and SAS
What other information, if any, do you need to prove the two triangles are congruent by SSS or SAS?
Postulate 4­2 Side­Angle­Side (SAS)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. A
D
C
B
G
E
Q
H
F
P
R
~
GHF = PQR
Given: AC and BD bisect each other
A
D
C
B
E
Nov 18­8:38 AM
~
~
Given: AB = CB, AD = CD
~
Proove: ABD = CBD
~
Given: AB = CB, BD bisects <B
~
Proove: ABD = CBD
B
B
A
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C
Which Postulate can we use, if any, to prove that the two triangle are congruent?
A
Which Postulate can we use, if any, to prove that the two triangle are congruent?
C
D
D
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2
4.2 Triangle Congruence SSS and SAS
Tell whether the triangles are congruent. If so, justify and write a congruence statement.
ex 3)
J
U
<
~
Given: JA // SY, JA = SY
~
Prove the triangles are =
Know:
A
J
<
Y
S
Found:
L
Y
ex 4)
M
A
Know:
<
<
H
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25.) Congruent? __________
24.) Congruent? __________
Assignment: Pg. 189­192 #1­4, 14­17, 22­27
If yes, Statement? _______________
Postulate? _______________
If no, Info needed? ________________
2.)
1.) 4.)
3.)
14.) SAS? ________________
SSS? ________________
26.) Congruent? __________
If yes, Statement? _______________
Postulate? _______________
16.) SAS? ________________
17.) SAS? ________________
SSS? _________________
SSS? _________________
If no, Info needed? ________________
22.) Congruent? __________
23.) Congruent? __________
If yes, Statement? _______________
Postulate? _______________
If yes, Statement? _______________
Postulate? _______________
If no, Info needed? ________________
If no, Info needed? ________________
If yes, Statement? _______________
Postulate? _______________
If no, Info needed? ________________
27.) Congruent? __________
15.) SAS? ________________
SSS? ________________
Nov 18­8:48 AM
Found:
T
If yes, Statement? _______________
Postulate? _______________
If no, Info needed? ________________
Nov 18­8:56 AM
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