Question

Prove that if each pair of opposite
sides of a quadrilateral is equal,
then it is
parallelogram​

Answer 1

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.

I hope it helped uu... Please mark me brainliest ☺️❤️..