Question

When angles of a pair of co-interior angles of a parallelogram are same, it forms a -

• A. rhombus
• B. rectanngle
• C. trapezoidal
• D. square

Answer 1

Answer: (B), (D)

square

Let us consider the following parallelogram:
We know that parallelograms have parallel opposite sides, hence $AD\&BC$ are transversal lines for parallel lines $AB\&CD$


The pair of co-interior angles associated with AD is $\angle a$ and $\angle b.$

From the co-interior angle theorem, $\angle a+\angle b={180}^o$

When $\angle a=\angle b,$ the above expression transforms to $\angle a+\angle a={180}^o$
$\Rightarrow 2\angle a={180}^o$
$\Rightarrow \angle a=\frac{{180}^o}{2}={90}^o$

$\therefore$ The transversal should make a right angle with the parallel lines, i.e., perpendicular.

The resulting figure is as follows:


$\therefore$ The parallelogram ABCD transforms into a rectangle on the given condition of equal co-interior angles.

A rhombus is a special type of parallelogram which doesn't have equal co-interior angles.

A square is also a prallelogram having parallel opposite sides, it have equal angles, hence it satisfy given condition of equal co-interior angles.
$\Rightarrow \angle 1=\angle 4=\angle 2=\angle 3$