What kind of quadrilateral is the shape shown here? [A] Rectangle only [B] Rectangle and square [C] Rhombus and rectangle [D] Parallelogram and rhombus [E] Parallelogram and rectangle.

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### Video Transcript

What kind of quadrilateral is the shape shown here? Rectangle only, rectangle and square, rhombus and rectangle, parallelogram and rhombus, or parallelogram and rectangle?

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.