begin mathsize 12px style increment space ABC space and space increment space ADC space are space two space right space triangles space with space common space hypotenuse space AC. space Prove space that space angle CAD space is space equal space to space angle CBD. end style

Asked by Topperlearning User | 4th Oct, 2017, 02:09: PM

Expert Answer:

 
 
 

ΔABC and ΔADC are right triangles with AC as common hypotenuse.

Two triangles together make a quadrilateral ABCD

In quadrilateral ABCD,

angle ABC + angle ADC = 90° + 90° = 180°

Now, sum of opposite angles of a quadrilateral is 180°.      (∵ by thm.)

∴ ABCD is a cyclic quadrilateral.

Then, angle CAD = angle CBD                    (∵ angles in the same segment of a circle are equal)

Answered by  | 4th Oct, 2017, 04:09: PM