Question

Prove that a cyclic parallelogram is always a triangle

Answer 1

Please note your question has an error, it is to prove the quadrilateral is a rectangle not a triangle because proving a quadrilateral is a triangle is just impossible (and an offence to math)

Given: ABCD is a cyclic parallelogram

To prove: ABCD is a rectangle

Proof:

Since ABCD is a parallelogram

⇒∠A=∠C------eq.1(opp. ∠s of a parallelogram are equal)

Also, ABCD is cyclic

⇒∠A+∠C=180(opp.∠s of a cyclic quad. are supplementary)

∴∠A+∠A=180(from eq.1)

2∠A=180

∠A=90

∵ABCD is a parallelogram with one angle = 90

∴ABCD is a rectangle