Question

In the figure D and E are the points on the base BC of triangle ABC such that BD= CD and AD=AE prove that triangle ABE is congruent to truangle ACD

Answer 1

Since in △AEC, CD = DE, AD is a median.

∴ ar(△ACD) = ar(△ADE) ---(i)

[∵ median divides a triangle into two triangles of equal areas]

Now, in △ABD , DE = EB, AE is a median     

∴ ar(△ADE) = ar(△AEB) ---(ii) 

From (i),(ii), we obtain 

ar(△ACD) = ar(△ADE) = ar(△AEB) = 1 / 3 ar(△ABC)

∴ ar(△ADE) = 1 / 3 × 27 = 9 cm2 

Answer 2

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