Question

. In the figure, PQRS is a quadrilateral. PQ is it's longest side and RS is the shortest side
prove that angle R is greater than angle P and angle Sless than angle Q
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Answer 1

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In the figure, PQRS is a quadrilateral. PQ is it's longest side and RS is the shortest side

prove that angle R is greater than angle P and angle Sless than angle Q.

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★Construction -: Join PR

In triangle PRS, RS is shortest side.

So, angle SPR is shortest angle opposite to stortest side to shotest.

➔Angle SRP↢Angle SPR

━━━━━━━━━━━━━━━━━━

In triangle PQR, PQ is the longest side.

So, angle PRQ is greatest angle opposite to longest side of greatest angle

➔Angle PRQ ↢Angle QPR

Angle SRP + Angle PRQ ↢Angle SPR + Angle QPR

Hence, Angle R ↢Angle P

═════════ ═════════

Hence proved!!

Answer 2

Answer:

In triangle PRS, RS is shortest side.

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.So, angle PRQ is greatest angle opposite to longest side of greatest angle

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.So, angle PRQ is greatest angle opposite to longest side of greatest angle➔Angle PRQ ↢Angle QPR

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.So, angle PRQ is greatest angle opposite to longest side of greatest angle➔Angle PRQ ↢Angle QPRAngle SRP + Angle PRQ ↢Angle SPR + Angle QPR

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.So, angle PRQ is greatest angle opposite to longest side of greatest angle➔Angle PRQ ↢Angle QPRAngle SRP + Angle PRQ ↢Angle SPR + Angle QPRHence, Angle R ↢Angle P

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.So, angle PRQ is greatest angle opposite to longest side of greatest angle➔Angle PRQ ↢Angle QPRAngle SRP + Angle PRQ ↢Angle SPR + Angle QPRHence, Angle R ↢Angle P═════════ ═════════

In triangle PRS, RS is shortest side.So, angle SPR is shortest angle opposite to stortest side to shotest.➔Angle SRP↢Angle SPR━━━━━━━━━━━━━━━━━━In triangle PQR, PQ is the longest side.So, angle PRQ is greatest angle opposite to longest side of greatest angle➔Angle PRQ ↢Angle QPRAngle SRP + Angle PRQ ↢Angle SPR + Angle QPRHence, Angle R ↢Angle P═════════ ═════════Hence proved!!