Question

In the given figure ABCD is a square and E is the midpoint of side AD . prove that angle ECB is equal to angle EBC.​

Answer 1

Given - ABCD is a square and E is mid point of side AD.

To Prove - angle ECB = angle EBC.

Proof - In triangle DEC and triangle AEB

DC = AB ( opp. side are equal )

AE = DE (because E is the mid-point of AD)

angle EAB = angle EDC (because right angle)

Therefore, Δ DEC ~ Δ AEB

And, angle ECB = angle EBC (By Corresponding parts of congruent triangle)

Hence Proved.

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