Question

prove that two sides of a cyclic quadrilateral are equal then the other two sides are parallel​

Answer 1

Answer :

We have to prove that if two opposite sides of a cyclic quadrilateral are equal then the other two sides are parallel.

Let PQRS be a cyclic quadrilateral with PS=QR, as shown in the figure.[See Attachment]

Construction: Extend PQ to U and draw RU⊥PQ. Draw PT⊥SR

In △PST and △RQU,

∠PST=∠RQU (exterior angle property of a cyclic quadrilateral).

PS=QR (given).

∠PTS=∠RUQ (by construction).

⇒△PST≅△RQU (AAS test).

⇒PT=RU (c.s.c.t.).

⇒PQ∥SR.

Therefore, if two opposite sides of a cyclic quadrilateral are equal then the other two sides are parallel.