`A B C` and `A D C` are two right triangles with common hypotenuse `A Cdot` Prove that `/_C A D=/_C B Ddot`

Explanation

`AC` is the common hypotenuse for two right triangles, `triangle ABC` and `triangle ADC`.
`angle ABC=angle ADC=90°`(Given)
`⇒angle ABC+angle ADC=180°`
(If the sum of a pair of opposite angles of a quadrilateral is `180°`, the quadrilateral is cyclic.)
Therefore, quadrilateral `ABCD` is cyclic.
`⇒angle CAD=angle CBD`.(Angles in the same segment are equal)