Geo4.4Glencoe.notebook
January 07, 2015
4.4 Target:
To identify congruent shortcuts
To write a flowchart proof
1
Geo4.4Glencoe.notebook
January 07, 2015
Assign 4.3 (page 256+)
9, 10, 13 ­ 16, 17 ­ 20, 23, 24, 28 ­ 30, 37
13) x = 20 14) y = 42, 15) z = 3, 16) w = 10 28) x = 12, y = 6 29) x = 13, y = 7 30) x = 4, y = 19
23) 37) yes...both are correct. Parts correspond.
24)
2
Geo4.4Glencoe.notebook
January 07, 2015
Are ∆'s congruent if we know that one side of a ∆ is congruent to a side
of another ∆?
Sketch an example or counter­example.
Are ∆'s congruent if we know that two sides of a ∆ are congruent to two sides of another ∆?
Sketch an example or counter­example.
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Geo4.4Glencoe.notebook
January 07, 2015
Are ∆'s congruent if we know that three sides of a ∆ are congruent to three sides of another ∆?
What would a construction look
like in this case?
YES -- Now ∆'s must
be congruent!
Knowing that three pairs of congruent
sides make a congruent triangle is called a
congruence shortcut.
S = side A = angle
There are other congruence shortcuts
based on comparing three parts of a
triangle.
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Geo4.4Glencoe.notebook
January 07, 2015
List the six possibilities (not all work):
(note...S = side, A = angle)
Today ...
SSS Congruence
If the 3 sides of one ∆ are congruent to the 3 sides of another ∆, then the ∆'s are congruent.
X
A
B
C
Z
Y
5
Geo4.4Glencoe.notebook
January 07, 2015
First ∆ proof using SSS:
M
A
B
C
N
P
Given: AB = MN
BC = NP
AC = MP
Prove: ∆ABC = ∆MNP
How to evaluate proofs:
Figure sketched & labeled
given/prove
Statements
Reasons
pathway noted
conclusion
6
Geo4.4Glencoe.notebook
January 07, 2015
N
M
P
O
R
P
Given: MN = NP
MO = OP
Prove: ∆MNO = ∆PNO
Given: See diagram
Prove: ∆PRT = ∆PWT
W
T
Group proof1
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Geo4.4Glencoe.notebook
Group proof2
January 07, 2015
B
Given: AB = BC. D bisects AC
Prove: ∆ABD = ∆CBD
A
D
C
SAS Congruence
If 2 sides and the included angle of one ∆ are congruent to 2 sides and the included angle of another ∆, then the ∆'s are congruent.
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Geo4.4Glencoe.notebook
January 07, 2015
4.4 P. 267 + 5, 6, 12, 13
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