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,
MN
QP
.
Since
M
is a right angle,
MQ
MN
. By the
Perpendicular Transversal Theorem,
MQ
QP
.
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:
EC
bisects
AD
.
AD
bisects
EC
.
Proof:
It is given that
ACDE
is a parallelogram.
Since opposite sides of a parallelogram are
congruent,
EA
DC
. By definition of a
parallelogram,
EA
DC
.
AEB
DCB
and
EAB
CDB
because alternate interior angles
are congruent.
EBA
CBD
by ASA.
EB
BC
and
AB
BD
by CPCTC. By the definition of
segment bisector,
EC
bisects
AD
and
AD
bisects
EC
.
45. Given:
WXYZ
Prove:
WXZ
YZX
Proof:
46. Given:
DGHK
is a parallelogram.
FH
GD
DJ
HK
Prove:
DJK
HFG
Proof:
47. Given:
BCGH
,
HD
FD
Prove:
F
GCB
Proof:
48.
MSR
PST
because they are vertical angles.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Angles, Right angle, Parallelogram

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