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Subjects
Mathematics CBSE
Class 9
Quadrilaterals
Quadrilaterals
5.
Prove the given statement
Exercise condition:
2
m.
In a quadrilateral \(ABCD\), \(AD = BC\) and \(\angle ADC = \angle BCD\). If \(M\) is the mid-point of \(CD\), then prove that \(AM = BM\).
S. No
.
Statement
Reason
1
.
\(AC = BD\)
\(AB = CD\)
\(AD = BC\)
Given
2
.
\(\angle AMD = \angle BMC\)
\(\angle AMC = \angle BMD\)
\(\angle ADM = \angle BCM\)
Since \(\angle ADC = \angle BCD\)
Since \(\angle ACD = \angle BDC\)
3
.
\(AM = BM\)
\(\angle ADC = \angle BCD\)
\(DM = CM\)
\(M\) is the mid-point of \(CD\)
4
.
\(\Delta ADC \cong \Delta BCD\)
\(\Delta ADM \cong \Delta BCM\)
by \(ASA\) congruence rule
by \(SSS\) congruence rule
by \(SAS\) congruence rule
5
.
\(AM = BM\)
\(AB = BC\)
\(AB = CD\)
by CPCT
Hence, proved
.
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