Question

Prove that an isosceles trapezium is always cyclic and its diagonals are equal.

Answer 1

In a cyclic trapezium,



∠BAD + ∠BCD = 180°

∠BAD + ∠ABC = 180°



∴ ∠ABC = ∠BCD



In ∆ABC and ∆BDC,



⇒∠ABC = ∠BCD

⇒∠BAC = ∠CDB (angles in the same segment)

⇒BC = BC (common side)

⇒∆ABC ≅ ∆BDC



∴ AB = CD and AC = BD



Hence, cyclic trapezium ABCD is isosceles and diagonals are equal to each other.

Hope it helps...!!!

Answer 2

cyclic trapezium abcd is isosceles and diagonals are equal to each other I hope it will help you