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

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

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

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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 \angleBAC = \angleBDC.

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.)

     \angleCAD = \angleCBD  (Angles in same segment are equal)

 

 

 

 

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