Question

In triangle ABC, D is mid-point of AB and P is any point on BC. If CA parallel to PD meets AB at Q, prove that:
2× area(∆ABC)= area (∆ABC)

Answer 1

I think this is the question u wanted to ask :

In ABC, D is the mid-point of

AB and P is any point on BC. If CQ || PD meets AB inthen prove that ar (BPQ) =1/2ar (ABC)

Solution:

In ABC, D is the mid-point ofAB and P is any point on BC. If CQ || PD me...

In triangle ABC, D is the mid-point of AB and P is any point on BC. If CQ || PD meets AB in Q then prove that ar (BPQ) =1/2ar (ABC)

Construction :- Join DC

To prove :- Since D is the mid-point of AB. so, in triangle ABC, CD is the median.

ar(triangle BCD = 1/2 ar (triangle ABC) ..... (1)

Since, triangle PDQ and triangle PDC are on the same base PD and between the same parallels lines PD QC.

therefore, ar(triangle PDQ) = ar(triangle PDC) ................ (2)

From (1) and (2)

ar(triangle BCD) = 1/2 ar(triangle ABC)

= ar(triangle BPD) + ar(triangle PDC) = 1/2ar(triangle ABC)

= ar(triangle BPD) + ar(triangle PDQ) = 1/2ar(triangle ABC) { area of triangle PDC = PDQ}

= ar(triangleBPQ) = 1/2 ar(triangle ABC)

Hence Proved ar(triangleBPQ) = 1/2 ar(triangle ABC).