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Maths CBSE Homework Assignments
Class 9
Quadrilaterals
Quadrilaterals I
3.
Prove the given statement
Question:
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
.
\(WZ = XY\)
\(WY = XZ\)
\(WX = YZ\)
Given
2
.
\(\angle WPZ = \angle XPY\)
\(\angle WZP = \angle XYP\)
\(\angle WPY = \angle XPZ\)
Since \(\angle WZY = \angle XYZ\)
Since \(\angle WYZ = \angle XZY\)
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 \(ASA\) congruence rule
by \(SAS\) congruence rule
by \(SSS\) congruence rule
5
.
\(WX = XY\)
\(WX = YZ\)
\(WP = XP\)
by CPCT
Hence, proved
.
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