Since, ABC and ADC are 2 right angle triangles with common hypotenuse AC i.e. angle B and angle D = 90
Hence, we can draw a circle passing through ABCD with AC as the diameter. (The angle subtended by the diameter of a circle on the circumference is 90)
Hence, now, DC is the chord of the circle and angle CAD and angle CBD are the angles subtended by the chord on the circumference of the circle.
Since, angles subtended by the same chord on the major arc of the circle are equal. So, angle CAD = angle CBD.