Question

ABC and ADC are two right triangles with common hypotenuse AC. Prove that ∠CAD = ∠CBD

Answer 1

 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.