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Maths CBSE Homework Assignments
Class 9
Quadrilaterals
Quadrilaterals I
3.
Prove the given statement
Task:
2
m.
In a quadrilateral \(PQRS\), \(PS = QR\) and \(\angle PSR = \angle QRS\). If \(M\) is the mid-point of \(RS\), then prove that \(PM = QM\).
S. No
.
Statement
Reason
1
.
\(PS = QR\)
\(PR = QS\)
\(PQ = RS\)
Given
2
.
\(\angle PMS = \angle QMR\)
\(\angle PSM = \angle QRM\)
\(\angle PMR = \angle QMS\)
Since \(\angle PRS = \angle QSR\)
Since \(\angle PSR = \angle QRS\)
3
.
\(\angle PSR = \angle QRS\)
\(PM = QM\)
\(SM = RM\)
\(M\) is the mid-point of \(RS\)
4
.
\(\Delta PSR \cong \Delta QRS\)
\(\Delta PSM \cong \Delta QRM\)
by \(SAS\) congruence rule
by \(ASA\) congruence rule
by \(SSS\) congruence rule
5
.
\(PQ = RS\)
\(PQ = QR\)
\(PM = QM\)
by CPCT
Hence, proved
.
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