Identify A polygon

Question

Choose ALL answers that describe the polygon EFGH if measure of angle E = 96 degrees, measure of angle F = 91 degrees, measure of angle G =89 degrees, measure of angle H =84 degrees, and side EF is parallel to side GH.

Choose ALL answers that describe the above polygon:

Parallelogram

Quadrilateral

Rectangle

Rhombus

Square

Trapezoid

Answer 1

Let's work through this problem by looking at each answer choice individually. It might be easier to understand the problem if we draw polygon EFGH on a piece of paper first. When we draw it, it looks like a four-sided closed polygon.

Is the polygon a parallelogram?

1. We know that a parallelogram has two pairs of parallel sides.
2. The polygon in the problem certainly has one pair of parallel sides since the problem tells us that side EF is parallel to side GH. But are the sides EH and FG parallel to each other? No, because they form different angles with the line that passes through H and G. Since sides EH and FG are not parallel to each other, this polygon cannot be a parallelogram.

Is the polygon a quadrilateral?

1. We know that a quadrilateral has four sides.
2. The polygon in the problem has four sides since it has four points: E, F, G, and H. It must be a quadrilateral.

Is the polygon a rectangle?

1. We know that a rectangle has four right angles.
2. Remember, a right angle is an angle that has a measure of 90 degrees. The polygon in the problem has angles that are not equal to 90 degrees, so it cannot be a rectangle.

Is the polygon a rhombus?

1. We know that a rhombus has opposite angles of equal measure. Opposite angles in a four-sided shape are the angles that are in opposite corners.
2. In the polygon from the problem, angles E and G are opposite, and F and H are opposite. E and G have different measures, and F and G have different measures. Because the measures of these angles differ, the polygon cannot be a rhombus.

Is the polygon a square?

1. We know that a square has four right angles (and four sides of equal length).
2. As we saw when we were asking if the polygon is a rectangle, the angles of the polygon in the problem are not right angles. Since the angles are not right angles, the polygon cannot be a square.

Is the polygon a trapezoid?

1. We know that a trapezoid has only one pair of parallel sides.
2. In the polygon from the problem, sides EF and GH are parallel to each other, so there is at least one pair of parallel sides. Now we need to check if the other pair of sides (EH and GH) are parallel. We can see that they are not parallel because they form different angles with the line that passes through H and G. The polygon has only one pair of parallel sides, so it is a trapezoid.

And we're done! We checked each answer choice, so we can now say that the polygon can be described as a quadrilateral and a trapezoid.