Question

Prove that a cyclic parallelogram is rectangular

Answer 1

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Given = ABCD is a cyclic parallelogram.

To prove = ABCD is a rectangle

Proof = In ∆ABC and ∆ADC

AB= CD

BC = AD

AC= AC

∆ABC is congruent to ∆ADC

< ABC =<ADC

In cyclic quadrilateral,

sum of opp. sides = 180

<ABC + <ADC= 180

<ABC + <ABC =180

2<ABC = 180

<ABC = 90

Similarly, all angle are 90

Hence, ABCD is a rectangle

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