CBSE Class 9 Answered
![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](https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=abfc7a7dd138a9aa0df3c55ff83d29e3.png)
Asked by Topperlearning User | 04 Oct, 2017, 14:09: PM
![](https://images.topperlearning.com/topper/questions/10209_image008.jpg)
ΔABC and ΔADC are right triangles with AC as common hypotenuse.
Two triangles together make a quadrilateral ABCD
In quadrilateral ABCD,
ABC +
ADC = 90° + 90° = 180°
Now, sum of opposite angles of a quadrilateral is 180°. (∵ by thm.)
∴ ABCD is a cyclic quadrilateral.
Then, CAD =
CBD (∵ angles in the same segment of a circle are equal)
Answered by | 04 Oct, 2017, 16:09: PM
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