Given : ABC and ADC are two right triangles with common hypotenuse AC.
To Prove : ∠CAD = ∠CBD
Proof : Let O be the mid-point of AC.
Then OA = OB = OC = OD
Mid point of the hypotenuse of a right triangle is equidistant from its vertices with O as centre and radius equal to OA, draw a circle to pass through A, B, C and D.
We know that angles in the same segment of a circle are equal.
Since, ∠CAD and ∠CBD are angles of the same segment.
Therefore, ∠CAD = ∠CBD. Proved.