Question

A point D is taken on the base BC of triangle ABC and AD is produced to E such that DE =AD . Show that area of triangle ABC is equal to the area of triangle BCE

Answer 1

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Answer 2

Median of Δ divides it into Two

Step-by-step explanation:

Given  : AD = DE

Construction : Join BE and CE

Proof :  

• InΔABE, Side is having BD (As a Median)

Now, ar(ΔBED) = ar(ΔBAD) [Median of a Δ divides it into 2 Δ's of equal areas]  ...(1)

• InΔACE, Side AE is having CD (As Median).

Now, ar(ΔECD) = ar(ΔACD)  [Median of a Δ divides it into 2 Δ's of equal areas]   ...(2)

adding (1) and (2), we get

ar(ΔBED) + ar(ΔECD)= ar(ΔBAD) +  ar(ΔACD)

⇒ar(ΔBEC) = ar(ΔABC)