Question

if a quad. each pair of opposite angle is equal then it is a llgm

Answer 1

yes it is a parallelogram

Answer 2

If each pair of opposite side of a quadrilateral is equal, then it is a llgm.

★$\mathfrak{\underline{\underline{Given:-}}}$

ABCD is a quadrilateral

AB=DC

AD=BC

★$\mathfrak{\underline{\underline{To\:prove:-}}}$

ABCD is a llgm i.e, we need to prove that ABllDC and AD ll BC.

★$\mathfrak{\underline{\underline{Proof:-}}}$

In ∆ABD and ∆BDC

AB=DC (given)

AD=BC (given)

BD=BD (common)

Therefore, ∆ABD congurent ∆BDC (SSS)

Therefore, angle 1 = angle 2 (cpct)----- 1.

which are alternate interior

therefore, ABllDC ------- 2.

Similarly,

• angle 3 = angle 4(cpct) ------- 3.

which are alternate angle

Therefore, AD ll BC ------- 4.

and from 1,2,3 and 4

ABCD is a llgm.