In a square ABCD, A is joined to a point X on BC and D is joined to a point Y on AB. If AX = DY, prove that AX is perpendicular to DY.

ABCD is a square. A is joined to a point P on BC and D is joined to a point Q on AB. If AP = DQ, prove that AP and DQ are perpendicular to each other.

ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that DX is perpendicular to AY.

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PB = QC

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PQ = QR

In the parallelogram ABCD ,M is mid-point of AC and X,Y are points on AB and DC respectively such that AX = CY. Prove that : (i) Triangle AXM is congruent to triangle (ii) XMY is a straight line.

ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that the triangles ADX and BAY are congruent.

ABCD is a square, X is the mid-point of AB and Y the mid-point of BC. Prove that angle DXA = angle AYB