Question

fill in the sentence below with the description that most specifically applies to the quadrilateral below.
answer attempt 1 out of 2
the quadrilateral is most specifically a , because

Explanation:

Step1: Identify side pairs

The quadrilateral has two sides of length 15 (opposite sides) and two sides of length 16 and 21? Wait, no, looking at the diagram, two sides are 15 (opposite), and the other two sides: wait, the labels are 15, 16, 15, and 21? Wait, no, maybe I misread. Wait, the quadrilateral has sides: 15, 16, 15, and 21? Wait, no, the arrows on 16 and 21 suggest that those sides are parallel? Wait, no, the arrows indicate parallel sides. Wait, the sides with 16 and 21 have arrows, meaning they are parallel, and the sides with 15 are opposite. Wait, no, let's re-express: the quadrilateral has two pairs of opposite sides? Wait, no, the lengths: two sides are 15 (so opposite sides equal), and the other two sides: 16 and 21? Wait, no, maybe the arrows are on the parallel sides. Wait, the side with 16 and the side with 21 have arrows, so they are parallel. And the sides with 15 are opposite. Wait, no, maybe the quadrilateral has two pairs of opposite sides: one pair is 15 (equal) and the other pair: wait, no, the diagram: let's see, the quadrilateral has vertices with sides: top side 15, right side 16 (with arrow), bottom side 15 (wait, no, the bottom side is 21? Wait, no, the left side is 21 (with arrow), right side 16 (with arrow), top side 15, bottom side 15? Wait, no, maybe I misread. Wait, the quadrilateral: two sides are 15 (so opposite sides equal), and the other two sides: 16 and 21? No, the arrows on 16 and 21 mean those sides are parallel. So, if two sides are parallel (16 and 21) and the other two sides are equal (15), then it's a trapezoid? No, wait, a parallelogram has both pairs of opposite sides parallel and equal. But here, the two sides with arrows (16 and 21) are parallel, and the other two sides (15) are equal and opposite. Wait, no, maybe the quadrilateral has two pairs of opposite sides: one pair is 15 (equal) and the other pair: 16 and 21? No, that can't be. Wait, maybe the correct approach: a parallelogram has opposite sides equal and parallel. But here, two sides are 15 (so opposite sides equal), and the other two sides: 16 and 21? No, that's not equal. Wait, maybe the arrows are on the equal sides? No, the arrows are for parallel. Wait, maybe the quadrilateral is a parallelogram? No, unless 16 and 21 are equal, but they are not. Wait, no, maybe I made a mistake. Wait, the problem: the quadrilateral has two sides of length 15 (opposite), and the other two sides: 16 and 21? No, the diagram: let's look again. The top side is 15, right side is 16 (with arrow), bottom side is 15 (wait, no, the bottom side is 21? No, the left side is 21 (with arrow), right side 16 (with arrow), top side 15, bottom side 15. So, the sides with arrows (16 and 21) are parallel, and the sides with 15 are equal and opposite. Wait, but 16 and 21 are not equal, so it's a trapezoid? No, a trapezoid has one pair of parallel sides. But here, if two sides are parallel (16 and 21) and the other two sides are equal (15), then it's an isosceles trapezoid? Wait, no, isosceles trapezoid has non-parallel sides equal. Wait, in an isosceles trapezoid, the non-parallel sides are equal, and the parallel sides are the bases. So, if the parallel sides are 16 and 21 (the bases), and the non-parallel sides are 15 (equal), then it's an isosceles trapezoid. Wait, but let's check: in an isosceles trapezoid, the legs (non-parallel sides) are equal, and the bases are parallel. So here, the sides with arrows (16 and 21) are the bases (parallel), and the other two sides (15) are the legs (equal). So that would make it an isosceles trapezoid. Alternatively, if it's a parallelogram, both pairs of opposite sides must be equal and parallel. But here, 16 and 21 are not equal, so it's not a parallelogram. So, the quadrilateral is an isosceles trapezoid because it has one pair of parallel sides (the ones with 16 and 21) and the non-parallel sides (the ones with 15) are equal in length.

Step2: Confirm the properties

An isosceles trapezoid is a trapezoid with the non-parallel sides (legs) equal in length and the base angles equal. Here, the two sides with length 15 are the legs (non-parallel), and the sides with 16 and 21 are the bases (parallel). Since the legs are equal, it's an isosceles trapezoid.

Answer:

The quadrilateral is most specifically a \boxed{isosceles trapezoid}, because it has one pair of parallel sides (the sides labeled 16 and 21) and the non - parallel sides (the sides labeled 15) are equal in length.