Question

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

Answer 1

Answer:

Step-by-step explanation:

Given: D is the midpoint of AB and P Point is any point on BC, CQ‖ PD

In Quadrilateral DPQC

Area (Δ DPQ) = Area (Δ DPC)

Add Area (Δ BDP) on both sides

We get,

Area (Δ DPQ) + Area (Δ BDP) = Area (Δ DPC) + Area (Δ BDP)

Area (Δ BPQ) = Area (Δ BCD) –1

D is the midpoint BC, and CD is the median

∴ Area (Δ BCD) = Area (Δ ACD) = 1/2 × Area (Δ ABC) –2

Sub –2 in –1

Area (Δ BPQ) = 1/2 × Area (Δ ABC) (∵Area (Δ BCD) = 1/2 × Area (Δ ABC))

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