Prove that a quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel.
Text Solution
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Given `AB||CD` with transversal `AC`
`/_BAC=/_DCA` (alternate angles)
In `/_\ADC` and `/_\CBA`
`AB+CD` (given)
`/_BAC=/_DCA` (alternate angles)
`AC=CA` (common)
By SAS congruency rule, `/_\ADC` and `/_\CBA` are congruent. Thus,
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