Question

If one pair of OPPOSITE sides of quadrilateral are equal and parralel then prove that it is a parralleogram

Answer 1

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, it is a parallelogram. If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.

Answer 2

Answer:

Proof : In ∆ACD and ∆CAB

1. AD = CB (Given)

2. AC = CA (Common side)

3. CD = AB (Given)

So, ∆ACD = ∆CAB (by SSS)

Step-by-step explanation:

$\sf \large Given :$

$\text{ABCD is a quadrilateral}$

AB = CD , BC = AD

$\text{To prove : ABCD is a parallelogram}$

Construction : Join A to C

Proof : In ∆ACD and ∆CAB

1. AD = CB (Given)

2. AC = CA (Common side)

3. CD = AB (Given)

$\green{ \sf \: So, ∆ACD = ∆CAB (by SSS) }$

:-∠1 = ∠2 and ∠3 = ∠4 (C.P.C.T)

As alternate angles are equal. So, sides will be parallel

⇒ AB || CD and AD || BC

⇒ ABCD is a parallelogram as both pairs of opposite

sides are parallel.