Question

Must quad. EFGH be a parallelogram? Can it be a parallelogram? Explain.

Short answer

EFGH is a not parallelogram.

Step-by-step solution

Step 1. Take information from the question

The figure shows a quadrilateral EFGH such that$\angle HEF=65°$and $\angle EHG=115°$.

Step 2. Find the sum of the given angles

Find the sum of the above two angles.

$\begin{array}{c}\angle HEF+\angle EHG=65°+115°\\ =180°\end{array}$

As per Theorem 3.6, if two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Step 3. Check whether EFGH is a parallelogram

For quadrilateral EFGH, HG and EF are cut by transversal HE and same-side interior angles are supplementary.

Therefore,$HG\parallel EF$

However, nothing more can be determined about quadrilateral EFGH.

Therefore, quadrilateral EFGH cannot be a parallelogram.