Question

Which is the most accurate description of the polygon?

Answer 1

Let’s take a look at the definitions of all of these categories of polygon:

A rhombus is a quadrilateral with four equal-length sides

A trapezoid is a quadrilateral with at least one pair of parallel sides

A kite is a quadrilateral with two pairs of equal sides, where those sides are adjacent to each other

A quadrilateral is a four-sided polygon

And let’s compare our definitions with the figure:

- None of the sides of the figure are equal to each other, so we it can’t be a rhombus
- The slopes of all of the sides are different, so the figure can’t have a pair of parallel lines, ruling out the chance that it’s a trapezoid
- That first bullet point also rules out the possibility that our figure is a kite
- Our figure *is* a four-sided polygon though, so it meets the requirements for a quadrilateral

So, the only label that works for this figure is a *quadrilateral*.