Q. 123.8( 13 Votes )

In the given figu

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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