2017 · Q99
ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements :
- 1Triangles ADX and BAY are congruent.
- 2∠DXA = ∠AYB.
- 3DX is inclined at an angle 60° with AY.
- 4DX is not perpendicular to AY.
Which of the above statements are correct ?
Elementary MathematicsQuadrilaterals and Polygons
- A2, 3 and 4 only
- B1, 2 and 4 only
- C1, 3 and 4 only
- D1 and 2 only
Explanation
Statement 1: AD = AB, AX = BY (half-sides), right angles at A and B give ΔADX ≅ ΔBAY by SAS — true. Statement 2 follows as corresponding angles — true. Coordinates give DX ⊥ AY (direction vectors (1,−2)·(2,1) = 0), so statements 3 and 4 are false. Hence 1 and 2 only: option D.