What kind of quadrilateral is the shape shown here? Rectangle only, rectangle and
square, rhombus and rectangle, parallelogram and rhombus, or parallelogram and
So there are four different types of quadrilateral that are listed in various
combinations in the options: rectangle, square, rhombus, and parallelogram. We need to look at the properties that are shown for this quadrilateral in order to
determine what kind of quadrilateral it is.
First, we know that opposite sides of this quadrilateral are parallel to each
other. This doesn’t actually help with narrowing down our choices because all four of the
types of quadrilateral listed are actually parallelograms.
Next, we know that whilst opposite pairs of sides are equal in length, which is true
of all parallelograms, not all four of the sides are the same. Seven is not equal to 13. This means that the quadrilateral can’t be a square or a rhombus as both these types
of quadrilateral have four equal sides.
So we’re left with the possibility that this quadrilateral is a rectangle only or
it’s a parallelogram and a rectangle. First, we can just confirm that the quadrilateral is indeed a rectangle as it has
four right angles. It isn’t actually possible for the quadrilateral to be a rectangle but not a
parallelogram as all rectangles are parallelograms.
Therefore, the correct answer to this problem is the final option. This quadrilateral is both a parallelogram and a rectangle.