Question

In the figure,the point P bisects AB and DC.prove that

Answer 1

P bisect AB so AP=BP....similarly CP=DP......in triangle APC and triangle BPD ..AP=BP (given). CD=DP(given ).=and angle BPD =angle APC (vertically opposite angle) .so by SAS criteria triangles are congruent

Answer 2

Δ A P C ≅ Δ B DPD    

Hence proved.

Step-by-step explanation:

Given:

In the figure, the point P bisects AB and DC that means point P is the angle bisector of AB and DC.

PA=PB            

To prove,

ΔAPD≅ΔBPD

PA=PB                           [Given]

∠APC=∠BOD                [vertically opposite ange]

PD=PC                            [adjacent sides]

ΔAPD≅ΔBPD    [SAS congruency]

Hence proved.