In figure, if ∠D = ∠C, then it is true that ∆ADE ∼ ∆ACB? – InterviewSolution

InterviewSolution

1.

In figure, if ∠D = ∠C, then it is true that ∆ADE ∼ ∆ACB? Why?

Answer»

True

In ∆ADE and ∆ACB,

Given,

∠D = ∠C

∠A = ∠A [common angle]

As we know sum of all the angles of a triangle is equals to 180∘.

So, by angle sum property of triangle the third angle of both triangles must be equal.

∠E = ∠B

∴ ∆ADE ∼ ∆ACB [by AAA similarity criterion]

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