Question

In a triangle ABC, DE ∥ BC and AE = a, EC = b, Find the value of DE/BC.

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Answer 1

Given : In a triangle ABC, DE ∥ BC and AE = a, EC = b

To Find : Value of  DE/BC

Solution:

in Δ ADE & ΔABC

∠A = ∠A  common

∠D = ∠B   ( corresponding angles ∵ DE || BC )

∠E = ∠C   ( corresponding angles ∵ DE || BC )

=> Δ ADE ≈ ΔABC  ( AAA Similarity criteria )

Similar Triangles: corresponding angles are congruent and the corresponding sides are proportional

=> AE/AC = DE/BC

AC = AE + EC  = a + b

AE = a

=> a / (a + b) =  DE/BC

Value of  DE/BC  =  a / (a + b)

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Answer 2

Answer:

in a tringle Abc , DE bc then the value of EC is