Math, asked by Anonymous, 1 year ago

Prove that if two opposite sides of a cyclic quadrilateral are equal then the other two sides are parallel.

Answers

Answered by trisha10433

112

hey
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i solved it by using an easy method , any doubts kindly ask me

hope helped
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Attachments:

Anonymous: trisha

Anonymous: how Angle 1 and 2 are equal only DA and BC is forming them

Anonymous: any relation

trisha10433: in the question its given DA and BC are equal and both the arcs are forming <1 and <2 in the place of DA and BC we placed <1 and <2 and on seeing they are pair of alternate inetrior angles !!

Anonymous: Awesome :)

SmãrtyMohït: Easy but nice explanation

trisha10433: thnq:)

siddhartharao77: Nice Explanation sis!

trisha10433: thanks bro :)

Answered by Anonymous

Hello!!

Question:

Prove that if two opposite sides of a cyclic quadrilateral are equal then the other two sides are parallel.

Solution:-

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.

Attachments:

SmãrtyMohït: fig correct bro

SmãrtyMohït: cyclic quadrilateral

ykhushi: Plz help me

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