# Q: 11         ABC and ADC are two right triangles with common hypotenuse AC. Prove that                    $\small \angle CAD =\angle CBD$.

S seema garhwal

Given: ABC and ADC are two right triangles with common hypotenuse AC.

To prove : $\small \angle CAD =\angle CBD$

Proof :

Triangle ABC and ADC are on common base BC and $\angle$BAC = $\angle$BDC.

Thus, point A,B,C,D lie in the same circle.

(If a line segment joining two points subtends equal angles at two other points lying on the same side of line containing line segment, four points lie on the circle.)

$\angle$CAD = $\angle$CBD  (Angles in same segment are equal)

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