41. Given:
n
ABC
Prove:
m
/
CBD
5
m
/
A
1
m
/
C
Proof:
42. Given:
n
RST
/
R
is a right angle
Prove:
/
S
and
/
T
are complementary
Proof:
43. Given:
n
MNO
/
M
is a right
angle.
Prove:
There can be at
most one right
angle in a triangle.
Proof:
In
n
MNO
,
/
M
is a right angle.
m
/
M
1
m
/
N
1
m
/
O
5
180.
m
/
M
5
90, so
m
/
N
1
m
/
O
5
90. If
/
N
were a right angle,
then
m
/
O
5
0. But that is impossible, so there
cannot be two right angles in a triangle.
Given:
n
PQR
/
P
is obtuse.
Prove:
There can be at most one obtuse angle in
a triangle.
Proof:
In
n
PQR
,
/
P
is obtuse. So
m
/
P
.
90.
m
/
P
1
m
/
Q
1
m
/
R
5
180. It must be
that
m
/
Q
1
m
/
R
,
90. So,
/
Q
and
/
R
must be
acute.
44. Given:
/
A
>
/
D
/
B
>
/
E
Prove:
/
C
>
/
F
Proof:
45.
m
/
1
1
m
/
2
1
m
/
3
5
¬
180
4
x
1
5
x
1
6
x
5
¬
180
15
x
5
¬
180
x
5
¬
12
m
/
1
5
4(12) or 48
m
/
2
5
5(12) or 60
m
/
3
5
6(12) or 72
46.
Sample answer: The shape of a kite is symmetric. If
triangles are used on one side of the kite, congruent
triangles are used on the opposite side. The wings
of this kite are made from congruent right
triangles. Answers should include the following.
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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

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