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Prove that a quadrilateral is a parallel...

Prove that a quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel.

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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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Knowledge Check

  • For two statement p and q p : A quadrilateral is a parallelogram q : The opposite sides are parallel Then, the compound proposition, ''A quadrillateral is a parallelogram if and only if the opposite sides are parallel'' is represented by

    A
    `p vv q`
    B
    `p to q`
    C
    `p ^^ q`
    D
    `p harr q`

  • Assertion : Square is not a parallelogram. Reason : The opposite sides of a square are parallel.

    A
    If both assertion and reason are true and reason is the correct explanation of assertion.
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true but reason is false.
    D
    If assertion is false but reason is true

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