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