Question

Which of the following statements given below are correct for parallelogram?

• A. Diagonals bisect each other
• B. pair of opposite sides are equal
• C. All angles are equal
• D. Sum of two adjacents angles is always ${180}^o$

Answer 1

Answer: (A), (B), (D)

Sum of two adjacents angles is always ${180}^o$

Parallelogram is the special type of quadrilateral which has pair of opposite sides parallel and equal.

$ABCD$ is the parallelogram and here, and $AC$, $BD$ are diagonals intersect at point $O$.

$AB=CD$, $BC=AD$
and, $AB||CD$, $BC||AD$

As, $AD||BC$,
$\angle DAB+\angle ABC={180}^o$ ( Co-interior angles)
So, two adjacent angles sums to ${180}^o$.

Now, in triangles $△AOB$ and $△COD$
$AB=CD$
$\angle OAB=\angle OCD$(alternate int. angles)
$\angle OBA=\angle ODC$(alternate int. angles)
So, $△AOB\cong △COD$(ASA)

$\Rightarrow AO=CO\text{and}BO=DO(C.P.C.T)$
So, we can say that $O$ is the midpoint of $AC$ and $BD$
Hence, diagonals of parallelogram bisect each other.

All angles of parallelogram are not equal but pair of opposite angles are equal. so option $\left(c\right)$ is not correct.

Hence, option $\left(a\right)$, $\left(b\right)$ and $\left(d\right)$ correct.