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38. Reflexive Property of Similarity
Given:
n
ABC
Prove:
n
ABC
,
n
ABC
Proof:
Symmetric Property of Similarity
Given:
n
ABC
,
n
DEF
Prove:
n
DEF
,
n
ABC
Proof:
Transitive Property of Similarity
Given:
n
ABC
,
n
DEF
and
n
DEF
,
n
GHI
Prove:
n
ABC
,
n
GHI
Proof:
39.
/
MKO
>
/
MOP
because they are both right
angles, and
/
M
>
/
M
,so
n
MKO
,
n
MOP
by AA
Similarity.
/
OKP
is a right angle because it forms
a linear pair with right angle
/
MKO
.
/
OKP
>
/
MOP
and
/
P
>
/
P
,so
n
MOP
,
n
OKP
by AA Similarity. Then
n
MKO
,
n
OKP
by
transitivity.
}
M
OK
K
}
5
¬
}
O
K
K
P
}
}
1
4
.
.
5
5
}
5
¬
}
K
4.
P
5
}
1.5(
KP
)
5
¬
4.5(4.5)
1.5(
KP
)
5
¬
20.25
KP
5
¬
13.5
The distance
KP
is 13.5 feet.
40.
If the side of
n
DEF
that is 36 cm corresponds to
the shortest side of
n
ABC
,then we can find the
lengths of the other sides of
n
DEF
using
proportions.
}
3
4
6
}
5
¬
}
6
x
}
36(6)
5
¬
4
x
216
5
¬
4
x
54
5
¬
x
}
3
4
6
}
5
¬
}
9
y
}
36(9)
5
¬
4
y
324
5
¬
4
y
81
5
¬
y
The perimeter of
n
DEF
is 36
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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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