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

Given,AC is the common hypotenuse.∠B=∠D=90°.To prove,∠CAD=∠CBDProof:Since,∠ABCand∠ADCare90°.These angles are in the semi-circle.Thus, both the triangles are lying in the semi-circle andACis the diameter of the circle.⇒ PointsA,B,CandDare concyclic.Thus,CDis the chord.⇒∠CAD=∠CBD...Angles in the same segment of the circle