Question

CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION?

Jason is asked to draw a quadrilateral with the following specifications.

two adjacent angles are acute and congruent
opposite angles are supplementary

Which of the following statements about this quadrilateral is true?
A.
Exactly one quadrilateral exists with the given conditions, and it must be a parallelogram.

B.
More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.

C.
Exactly one quadrilateral exists with the given conditions, and it must be an isosceles trapezoid.

D.
More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.

Answer 1

B. More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.

Explanation:

In a parallelogram, adjacent angles are supplementary. They are only congruent if the parallelogram is a rectangle. In this problem, adjacent angles are both congruent and acute. If this were a triangle, it would guarantee the triangle is isosceles.

The fact that opposite angles are supplementary guarantees that the fourth side of the figure is parallel to the base between the acute angles. That makes the figure an isosceles trapezoid. Unless specific angles and side lengths are specified, the description matches any isosceles trapezoid.