Question

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

Answer 1

According to the question,

We have,

ACB and ADB are two right triangles.

To Prove: ∠BAC = ∠BDC

We know that,

ACB and ADB are right angled triangles,

Then,

∠C + ∠D = 90° + 90°

∠C + ∠D = 180°

Therefore ADBC is a cyclic quadrilateral as sum of opposite angles of a cyclic quadrilateral = 180°

We also have,

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

∴ ∠BAC = ∠BDC.

Hence Proved.