in the diagram, AB= BC. Prove that ABCD is a cyclic quadrilateral. Give reasons for any statements you make

Step-by-step explanation:

Given : AB = BC.

To Prove : ABCD is a cyclic quadrilateral.

Solution : AB ≅ CD [Given]

m∠BAC = m∠BCA = x° [Property of an isosceles triangle]

m∠ABC = 180° - (m∠BAC + m∠ACB) [Triangular sum theorem]

m∠ABC = 180° - (x + x)

              = 180° - 2x°

m∠ABC + m∠ADC = (180 - 2x) + 2x

                               = 180°

[Property of cyclic quadrilateral → Sum of opposite angles = 180°]

Hence proved.