Question

Q23. In triangle ABC, E is the mid point of AD. Show that ar(BED)= ar (ABC)
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Answer 1

Answer:

E is the mid point of AD.

Therefore,

it will divide ΔABC into two triangles of equal area.

∴ Area (ΔABD) = Area (ΔACD)

⇒Area (ΔABD ) = (½) area (Δ ABC) ------------(1)

In ΔABD, E is the mid-point of AD.

Therefore, BE is the median.

∴ Area (ΔBED) = Area (ΔABE)

Area (ΔBED) = (1/2)Area (ΔABD)

Area (ΔBED) = (½ ) x(1/2) Area (ΔABC) [From (1)]

∴ Area (ΔBED) = (1/4)Area (ΔABC).

Hence, prove

Step-by-step explanation:

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