Question

In Fig 2, AP=PD and CP=PB. Show that
(i) ∆APB ~∆CPD
(ii) AB || CD

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Answer 1

Step-by-step explanation:

Given :- AP = PD and CP=PB

To prove :- i) ∆APB ~∆CPD and ii) AB || CD

Solution:-

i) In ∆APB and ∆CPD,

AP=PD (GIVEN)

BP =CP (GIVEN)

∠APB = ∠CPD (Vertically Opp. Angles)

Therefore, ∆APB ~∆CPD (by SAS rule)

AB = CD & ∠CDP =∠BAP (CPCT)

ii) AB || CD

Since, ∠CDP =∠BAP (CPCT), AB and CD are parallel.

Therefore, AB || CD.

(I am not sure about the (ii) answer)

Hope this helps you!!