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

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

Proof: ∵ AC is the common hypotenuse, ABC and ADC are two right triangles.
∴ ∠ABC = 90° = ∠ADC
⇒ Both the triangles are in the same semicircle.
∴ Points A, B, D and C are concyclic.
∵ DC is a chord
∴ ∠CAD = ∠CBD.
| ∵ Angles in the same segment are equal.