in triangle ABC D id the mid-point of AB P is any point on BC if CQ is parallel - Maths - Areas of Parallelograms and Triangles

Question

in triangle ABC D id the mid-point of AB &P is any point on
BC if CQ is parallel to PD meets AB in Q,then prove that :-

ar(BPQ)=1/2ar(ABC

Priyanka Kedia · Accepted Answer

Given that: ABC is a triangle and D is the mid-point of AB and P is a point on BC such that PD||CQ To Prove:

Construction: join C to D proof: Since D is mid-point on AB, so CD is a median of the

Thus,

Now

and

are on the same base PD and between the same parallels PD and CQ So,

From equation (1), we get,

So,

Hence,

in triangle ABC.D id the mid-point of AB &P is any point on BC.if CQ is parallel to PD meets AB in Q,then prove that :- ar(BPQ)=1/2ar(ABC