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Question

# Given a square of one unit side length. Four points are chosen on the square as shown. Then the quadrilateral EFGH so formed is a

A

Square

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B

Parallelogram

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C

Rhombus

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D

Rectangle

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Solution

## The correct option is A Square Using Phythagoras theorem in Δ AEH we get EH=√104 Similarly we can get EH = FG = EF = GH In ΔAEH and ΔHDG AH = DG AE = DH ∠ EAH = ∠ HDG (900) Δ EAH ≅Δ HDG Let ∠ AHE = x0 Then ∠ DGH = x0 ∠ DHG = 900−x0 (Using sum of angles in a triangle is 1800) ∠EHG = 900 (using sum of angles on a straight line) Similarly we can prove others also. So EHGF is a square.

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