Question

Theorem 8.8 :A quadrilateral is a parallelogram if a pair of opposite sides is
equal and parallel.​

Answer 1

A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.​

Step-by-step explanation:

Let say ABCD is a parallelogram

AB = CD  & AB ║ CD

Join AC

as AB ║ CD

=> ∠BAC = ∠DCA

Δ BAC & Δ DCA

AB = CD

∠BAC = ∠DCA

AC = AC ( common)

=> Δ BAC ≅ Δ DCA

=> BC = AD

∠BCA = ∠DAC  => (AD ║ BC)

Now AB = CD  & AB ║ CD  

also BC = AD  & AD ║ BC

=> ABCD is a parallelogram

QED

Hence Proved

A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.​

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