Question

If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.Prove it.​

Answer 1

Answer:

theorem::If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.Prove it.​

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.

Answer 2

Step-by-step explanation:

given:-

AB=CD and BC=AD

JOIN AC

TO PROVE:-

angle A= angle C

angle B =angle D

PROVE:-

IN ∆ABC and ∆CDA

AB= CD (given)

BC=AD(opposite sides)

AC=CA (common)

SO, ∆ABC CONGRUENT TO ∆CDA(BY S.S.S RULE)

SO, angle A = angle C & angle B = angle D