Download 4.2 Triangle Congruence SSS and SAS

4.2 Triangle Congruence SSS and SAS
November 18, 2014
Nov 18­8:38 AM
D.I.R.T?
1) Given figure DEFG NSTP, list all the congruent parts.
Given figures MNOW BDCR, fill in the blanks.
M
10
N
D
C
100
O
15
W
B
R
2) BD=_________
3) m<C=__________
4) MW ________
5) m<M=__________
6) <R ________
7) OW= ___________
Nov 18­8:28 AM
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4.2 Triangle Congruence SSS and SAS
November 18, 2014
Find the missing variable.
Nov 6­10:07 AM
4.2 Triangle Congruence by SSS and SAS
Objective: To prove two triangles congruent using the SSS and SAS Postulates
Postulate 4­1 Side­Side­Side (SSS)
If three sides on one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Q
H
G
F
P
R
~
GHF = PQR
Nov 18­8:29 AM
2
4.2 Triangle Congruence SSS and SAS
November 18, 2014
The word included used frequently when referring to angles and side of a triangle.
A
Given the two sides, what is the included angle?
AC and AB AC and CB _____________
<B is included by which two sides? _________
Given the two angles, what is the included side?
<A and <B ______________
C
<B and <C _____________
B
AC is the included side for which two angles? ______________
Nov 18­8:32 AM
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. Q
H
G
F
P
R
~
GHF = PQR
Nov 18­8:38 AM
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4.2 Triangle Congruence SSS and SAS
November 18, 2014
What other information, if any, do you need to prove the two triangles are congruent by SSS or SAS?
A
D
C
B
E
Given: AC and BD bisect each other
A
D
C
B
E
Nov 18­8:41 AM
~
~
Given: AB = CB, AD = CD
~
Proove: ABD = CBD
B
A
C
Which Postulate can we use, if any, to prove that the two triangle are congruent?
D
Nov 18­8:43 AM
4
4.2 Triangle Congruence SSS and SAS
November 18, 2014
~
Given: AB = CB, BD bisects <B
~
Proove: ABD = CBD
B
Which Postulate can we use, if any, to prove that the two triangle are congruent?
A
C
D
Nov 18­8:45 AM
~
Given: JA // SY, JA = SY
Prove the triangles are =~
A
J
S
Y
Nov 18­8:46 AM
5
4.2 Triangle Congruence SSS and SAS
November 18, 2014
Tell whether the triangles are congruent. If so, justify and write a congruence statement.
ex 3)
J
<
Y
ex 4)
U
<
Know:
Found:
L
M
A
Know:
<
<
H
T
Found:
Nov 18­8:47 AM
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