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)

Question

In Fig. 15.90, D and E are two points on BC such that BD=DE=EC. Show that ar(&#x394; ABD) = ar(&#x394; ADE) =ar(&#x394; AEC)

Philoid · Accepted Answer

Draw a line through A parallel to BC

Given that,

BD = BE = EC

We observed that the triangles ABD and AEC are on the same base and between the same parallels l and BC

Therefore, their areas are equal

Hence,

Area () = Area () = Area ()