Question

If ABCD is a parallelogram, then which of the following is true?

• A. AC=BD
• B. AB=AC
• C. $\angle A={130}^{\circ },\angle C={130}^{\circ },\angle B={50}^{\circ }$
• D. $AB\perp AD$

Answer 1

The correct option is C

$\angle A={130}^{\circ },\angle C={130}^{\circ },\angle B={50}^{\circ }$

In a parallelogram, the adjacent sides and angles are not equal and no sides are perpendicular to other.

$\angle A+\angle B={130}^{\circ }+{50}^{\circ }={180}^{\circ }$
Here, $\angle A$ and $\angle B$ are co-interior angles and their sum is ${180}^{\circ }$.
By the converse of co-interior angles theorem, AD || BC and AB is the transversal.

$\angle D+\angle A={50}^{\circ }+{130}^{\circ }={180}^{\circ }$
Here, $\angle D$ and $\angle A$ are co-interior angles and their sum is ${180}^{\circ }$.
By the converse of co-interior angles theorem, AB || DC and AD is the transversal.