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32. Given:
n
MNO
is an
equilateral triangle.
Prove:
m
/
M
5
m
/
N
5
m
/
O
5
60
Proof:
33. Given:
n
ABC
/
A
>
/
C
Prove:
A
w
B
w
>
C
w
B
w
Proof:
34.
The minimum requirement is that two angles
measure 60°.
35.
The front face of the figure has two congruent
angles and one angle of measure 60. Let
y
represent
the measure of each of the congruent angles.
y
1
y
1
60
5
¬
180
2
y
1
60
5
¬
180
2
y
5
¬
120
y
5
¬
60
Therefore all angles have measure 60, so the
triangle is equiangular and equilateral. All sides
have length 2
x
1
5, in particular the edge
between the front face and the side face showing.
Because the side face has two congruent base
angles it is isosceles and the sides opposite the
congruent angles are congruent.
2
x
1
5
5
¬
3
x
2
13
2
x
1
18
5
¬
3
x
18
5
¬
x
36.
The triangle is isosceles with base angles having
measure 3
x
1
8.
(3
x
1
8)
1
(3
x
1
8)
1
(2
x
1
20)
5
¬
180
8
x
1
36
5
¬
180
8
x
5
¬
144
x
5
¬
18
37.
The triangle on the bottom half of the figure is
isosceles. The base angles are congruent.
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles

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