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247
Chapter 8
43. Given:
~
MNPQ
/
M
is a right angle.
Prove:
/
N
,
/
P
and
/
Q
are right angles
Proof:
By definition of a parallelogram,
M
w
N
w
i
Q
w
P
w
.
Since
/
M
is a right angle,
M
w
Q
w
'
M
w
N
w
.By the
Perpendicular Transversal Theorem,
M
w
Q
w
'
Q
w
P
w
.
/
Q
is a right angle, because perpendicular lines
form a right angle.
/
N
>
/
Q
and
/
M
>
/
P
because opposite angles in a parallelogram are
congruent.
/
P
and
/
N
are right angles, since all
right angles are congruent.
44. Given:
ACDE
is a parallelogram.
Prove:
E
w
C
w
bisects
A
w
D
w
.
A
w
D
w
bisects
E
w
C
w
.
Proof:
It is given that
ACDE
is a parallelogram.
Since opposite sides of a parallelogram are
congruent,
E
w
A
w
>
D
w
C
w
.By definition of a
parallelogram,
E
w
A
w
i
D
w
C
w
.
/
AEB
>
/
DCB
and
/
EAB
>
/
CDB
because alternate interior angles
are congruent.
n
EBA
>
n
CBD
by ASA.
E
w
B
w
>
B
w
C
w
and
A
w
B
w
>
B
w
D
w
by CPCTC. By the definition of
segment bisector,
E
w
C
w
bisects
A
w
D
w
and
A
w
D
w
bisects
E
w
C
w
.
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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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