RepeaTheorem 8.3: If each pair of opposite sides of a quadrilateral is

1.	RepeaTheorem 8.3: If each pair of opposite sides of a quadrilateral is equal, then itis a parallelogram.Eac
Answer» Given: A quadrilateral ABCD in which To Prove: ABCD is a parallelogram i.e., AB ║ DC and AD ║ BC Construction : Join A and C Proof : In ∆ABC and ∆CDA AB = DC [Given] AD = BC [Given] And AC = AC [Common] ∴ ∆ABC ≅ ∆CDA [By SSS] ⇒ ∠1 = ∠3 [By cpctc] And ∠2 =∠4 [By cpctc] But these are alternate angles and whenever alternate angles are equal, the lines are parallel. ∴ AB ║ DC and AD ║ BC ⇒ ABCD is a parallelogram.

RepeaTheorem 8.3: If each pair of opposite sides of a quadrilateral is equal, then itis a parallelogram.Eac

Answer»

Given: A quadrilateral ABCD in which

To Prove: ABCD is a parallelogram i.e., AB ║ DC and AD ║ BC

Construction : Join A and C

Proof : In ∆ABC and ∆CDA

AB = DC [Given]

AD = BC [Given]

And AC = AC [Common]

∴ ∆ABC ≅ ∆CDA [By SSS]

⇒ ∠1 = ∠3 [By cpctc]

And ∠2 =∠4 [By cpctc]

But these are alternate angles and whenever alternate angles are equal, the lines are parallel.

∴ AB ║ DC and AD ║ BC

⇒ ABCD is a parallelogram.