in ∆abc,median AD is produce to point P such that AD=DP.prove that ABPC is a parallelogram
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Given,AD = DP
and BD = DC(since AD is the median)
angle BDP = angle ADC ( since opposite angles)
Therefore by SSS congruency , ∆BDP≈∆CPA
Therefore BP = AC
Similarly ∆BDA≈∆CDA
and AB=PC
In a quadrilateral if opposite sides are equal then the quadrilateral formed is a parallelogram
Therefore ABPC is a parallelogram
and BD = DC(since AD is the median)
angle BDP = angle ADC ( since opposite angles)
Therefore by SSS congruency , ∆BDP≈∆CPA
Therefore BP = AC
Similarly ∆BDA≈∆CDA
and AB=PC
In a quadrilateral if opposite sides are equal then the quadrilateral formed is a parallelogram
Therefore ABPC is a parallelogram
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