Question

In each exercise, you could prove that quadrilateral SANG is a parallelogram if one more fact, in addition to those stated were given. State the fact.

$\overline{\mathrm{SA}}\parallel \overline{\mathrm{GN}};\mathbf{SA}\mathbf{=}\mathbf{17}$

Short answer

The additional fact that must be given so that SANG can be a parallelogram is that the measure of the side GN must be 17.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

It is being given that $\overline{SA}\parallel \overline{GN}$and $SA=17$.

If one pair of opposite sides of a quadrilateral are both congruent and parallel then the quadrilateral is a parallelogram.

From the given diagram it can be observed that the pair of opposite sides of the quadrilateral SANG are SA, GN and SG, AN.

As, $\overline{SA}\parallel \overline{GN}$, that implies the opposite sides of the quadrilateral SA and GN are parallel.

Therefore, the SANG can be a parallelogram if the measure of the side GN is 17 so that the pair of opposite sides SA and GN are both congruent and parallel.

Therefore the measure of the side GN must be 17 so that SANG can be a parallelogram.

Step 3. Description of step.

Therefore, the additional fact that must be given so that SANG can be a parallelogram is that the measure of the side GN must be 17.