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