Question

Determine whether each quadrilateral is a parallelogram. Justify your answer. Yes/No? Reason... opposite side congruent, opposite angles congruent, opposite sides parallel, diagonals bisect each other, one pair of parallel and congruent sides, not enough information? (look at the image)

Answer 1

Yes! The given quadrilateral represents Parallelogram.

Reason: The given quadrilateral has opposite angles congruent.

Explanation:

Given the quadrilateral with the angles

• 118°

• 62°

• 62°

• 118°

We know that the sum of the angles of a quadrilateral is 360.

so

118°+62°+118°+62° = 360°

Thus, the given figure is indeed a quadrilateral.

Now in order to determine whether the given quadrilateral is a parallelogram or not, we need to check whether the opposite angles are congruent or not.

If the angles opposite of each other will have the same measurement, then the quadrilateral will represent Parallelogram.

It is clear that the given quadrilateral has two pairs of equal opposite angles.

i.e. The angle 118° has the same opposite angle 118° and the angle 62° has the same opposite angle 62°.

Therefore, the given quadrilateral represents Parallelogram.

Hence,

Yes! the given quadrilateral represents Parallelogram.

Reason: The given quadrilateral has opposite angles congruent.