Question

ABC and ADC are two right angles with common hypotenuse AC .prove that <CAD=<CBD

Answer 1

${Answer :-}$

Here, we have that both the triangles ABC and ADC are right angled triangles.

We know that the angle opposite to the hypotenuse of a right-angled triangle is 90 degree.

Thus, angle ABC = angle ADC = 90 degrees.

Now, we have quadrilateral ABCD.
Sum, of opposite angles is
angle ABC + angle ABD = 90 + 90 + 180 degrees.

Thus, in quadrilateral ABCD, sum of opposite angles is 180 degree. Therefore, it is a ${Cyclic}$ quadrilateral.

We have that angle CBD and angle CAD lie in the same segment.
Since, angles lying on the same segment are equal, so, angle CBD = angle CAD.

Hence, angle CAD = angle CBD (proved)

Hope this helps,.

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Answer 2

I hope you understand