Question

11. ABC and ADC are two right triangles with common hypotenuse AC. Prove that
ZCAD= ZCBD.
icomica rectangle​

Answer 1

Answer:

Given,

AC is the common hypotenuse. ∠B=∠D=90°.

To prove,

∠CAD=∠CBD

Proof:

Since, ∠ABC and ∠ADC are 90°.

These angles are in the semi-circle.

Thus, both the triangles are lying in the semi-circle and AC is the diameter of the circle.

⇒ Points A,B,C and D are concyclic.

Thus, CD is the chord.

⇒∠CAD=∠CBD ...Angles in the same segment of the circle