Question

Is quadrilateral ABCD a parallelogram, if $\angle A=70{}^\circ $ and $\angle C=65{}^\circ $ ? Give reason.

Answer 1

Hint: Think of the property of parallelogram which states opposite angles of parallelogram is equal.

Complete step-by-step answer:

In the question, we are given two approach angles which are $\angle A=70{}^\circ $ , $\angle C=65{}^\circ $ of ABCD. Now, we have to say whether the quadrilateral is parallelogram or not.

Before telling, we will first briefly tell characteristics of parallelogram.

A simple (non-self intersecting) quadrilateral is a parallelogram if and only if one of the following statements is true:

(a) Two pairs of opposite sides are parallel.
(b) Two pairs of opposite sides are equal in length.
(c) Two pairs of opposite angles are equal in measure.
(d) The diagonals bisect each other.
(e) One pair of opposite sides is parallel and equal in length.
(f) Adjacent angles are supplementary.
(g) The diagonals bisect into two congruent triangles.

In one of the characteristics it was given that opposite angles of parallelogram are equal.
Here, angle A and angle C are opposite angles of parallelogram. So, they should be equal but in the given question $\angle A$ is $70{}^\circ $ and $\angle C$ is $65{}^\circ $. So, the quadrilateral is not a parallelogram.

Hence, it is not a parallelogram.

Note: Students should know the properties of all the special quadrilaterals which may help to tackle this kind of question easily and so they can do them very smoothly.