On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠ BAC = ∠ BDC.

Question

Philoid · Accepted Answer

Given: ACB and ADB are two right triangles.

To Prove: ∠BAC = ∠BDC

Since ACB and ADB are right angled triangles, therefore

∠C + ∠D = 90° + 90°

= 180°

Therefore ADBC is a cyclic quadrilateral. (∵ Sum of opposite angles of a cyclic quadrilateral is 180°.)

Also, ∠BAC and ∠BDC lie in the same segment BC and angles in the same segment of a circle are equal.

∴ ∠BAC = ∠BDC.

Hence Proved.