Answer :

Observe in ∆BED & ∆ACB, we have

∠BED = ∠ACB = 90°

Now according to what’s given, DB ┴ BC and AC ┴ BC we can write,

∠B + ∠C = 180°

This clearly means BD ∥ CA

⇒ ∠EBD = ∠CAB [They are alternate angles]

**AA Similarity theorem:**The postulate states that two triangles are similar if they have two corresponding angles that are congruent or equal in measure.

Thus, by AA-similarity theorem, ∆BED ∼ ∆ACB

Now, by property of similarity of triangles,

So,

Cross-multiplying, we get,⇒

**Hence, proved.**

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