In ΔABC,
∠ABC + ∠BCA + ∠CAB = 180° (Angle sum property of a triangle)
∠90° + ∠BCA + ∠CAB = 180°
∠BCA + ∠CAB = 90° ... (1)
In ΔADC,
∠CDA + ∠ACD + ∠DAC = 180° (Angle sum property of a triangle)
∠ 90° + ∠ACD + ∠DAC = 180°
∠ACD + ∠DAC = 90° ... (2)
Adding equations (1) and (2), we obtain
∠BCA + ∠CAB + ∠ACD + ∠DAC = 180°
(∠BCA + ∠ACD) + (∠CAB + ∠DAC) = 180°
∠BCD + ∠DAB = 180° ... (3) However, it is given that
∠B + ∠D = 90° + 90° = 180° ... (4)
From equations (3) and (4), it can be observed that the sum of the measures of opposite angles of quadrilateral ABCD is 180°. Therefore, it is a cyclic quadrilateral. Consider chord CD.
∠CAD = ∠CBD (Angles in the same segment)
