ABCD is a square. X is the mid-point of AB

ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements:

  1. Triangles ADX and BAY are congruent
  2. ∠DXA = ∠AYB
  3. DX is inclined at an angle 60° with AY
  4. DX is not perpendicular to AY

Which of the above statements are correct?

  1. 2, 3 and 4 only
  2. 1, 2 and 4 only
  3. 1, 3 and 4 only
  4. 1 and 2 only

Answer

By RHS rule,

Δ ADX ≅ Δ BAY

Triangles ADX and BAY are congruent.

Also, DX is perpendicular to AY.

The correct option is D.