Maths-

General

Easy

Question

# PQ and RS are respectively the smallest and longest sides of a quadrilateral PQRS. Show that ∠ P > ∠ R

Hint:

### Hint :-As we know angles opposite longer sides are greater

Angle opposite to smaller sides are smaller

## The correct answer is: Hence proved

### Aim :- Prove ∠P ∠R

In triangle PQR,

PQ < QR (PQ is smallest)

so, ∠PRQ ∠QPR

In triangle PSR,

PS < SR (RS is longest side)

∠ PRS ∠ RPS

Adding above results we get,

∠PRQ + ∠PRS ∠QPR + ∠RPS

∠R ∠P

Hence proved

In triangle PQR,

PQ < QR (PQ is smallest)

so, ∠PRQ ∠QPR

In triangle PSR,

PS < SR (RS is longest side)

∠ PRS ∠ RPS

Adding above results we get,

∠PRQ + ∠PRS ∠QPR + ∠RPS

∠R ∠P

Hence proved

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