Question

In Fig. 15.90, D and E are two points on BC such that BD=DE=EC. Show that ar(Δ ABD) = ar(Δ ADE) =ar(Δ AEC)

Answer 1

Given:  

ABC is a Triangle , D & E are two Points on BC, Such that BD = DE = EC

To Prove:

ar (ABD) = ar (ADE) = ar (AEC)

Proof:

Let AO be the perpendicular to BC.

We know that,

Area of ∆ = ½ × base × height

ar(∆ABD) = ½ × BD × AO

ar(∆ADE) = ½ × DE × AO

ar(∆AEC) = ½ × EC × AO

BD = DE = EC [given]

ar(∆ABD) = ar(∆ADE) = ar(∆AEC)

Hence proved  

Hope this answer will help you …..

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