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Subjects
Mathematics CBSE
Class 9
Quadrilaterals
Quadrilaterals
5.
Prove the given statement
Exercise condition:
2
m.
In a quadrilateral
WXYZ
,
WZ = XY
and
\angle WZY = \angle XYZ
. If
P
is the mid-point of
YZ
, then prove that
WP = XP
.
S. No
.
Statement
Reason
1
.
WY = XZ
WZ = XY
WX = YZ
Given
2
.
\angle WPZ = \angle XPY
\angle WZP = \angle XYP
\angle WPY = \angle XPZ
Since
\angle WYZ = \angle XZY
Since
\angle WZY = \angle XYZ
3
.
\angle WZY = \angle XYZ
ZP = YP
WP = XP
P
is the mid-point of
YZ
4
.
\Delta WZY \cong \Delta XYZ
\Delta WZP \cong \Delta XYP
by
SAS
congruence rule
by
SSS
congruence rule
by
ASA
congruence rule
5
.
WX = XY
WX = YZ
WP = XP
by CPCT
Hence, proved
.
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