Video: AF5P1-Q07-310126301694v2

This quadrilateral is drawn accurately. What type of quadrilateral is it? Tick all boxes that apply. [A] Parallelogram [B] Rectangle [C] Square [D] Rhombus [E] Regular quadrilateral

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Video Transcript

This quadrilateral is drawn accurately. What type of quadrilateral is it? Tick all boxes that apply. Parallelogram, rectangle, square, rhombus, regular quadrilateral.

Let’s firstly consider the five quadrilaterals listed and their specific properties. Let’s firstly consider a regular quadrilateral. Any polygon is said to be regular if all of its sides are equal in length. We also require all the angles to be equal. This means that a regular quadrilateral is in fact a square as this is the only quadrilateral where all four sides are equal in length and all four angles are equal, in this case 90 degrees.

We now need to consider the similar and different properties of the four shapes, parallelogram, rectangle, square, and rhombus. All four of the shapes have two pairs of parallel sides. A rectangle and a square have 90-degree angles whereas a rhombus does not. Both a rhombus and a square have four sides of equal length, whereas this time a rectangle does not. This leads us to some very important facts about quadrilaterals. Every rhombus, rectangle, or square is actually a parallelogram whereas the opposite is not the case. Likewise, every square is a rectangle. But not every rectangle is a square.

Let’s now consider the shape that has been drawn. If it is a rhombus, square, or rectangle, then it will also be a parallelogram. The marks on each side of the quadrilateral indicate that each of the sides is equal in length. This rules out rectangle as one of the options. The shape has two pairs of parallel sides. This however does not narrow down our options as all of the shapes have two pairs of parallel sides. The opposite angles inside the shape are equal. However, they are not right angles. Therefore, they are not 90 degrees. This means that we can rule out square as a square has to have four 90-degree angles. As a square is the only type of regular quadrilateral, we can also rule out this option.

The shape that is drawn is a rhombus as it has two pairs of parallel sides and four equal length sides. Whilst the shape doesn’t match our usual diagram for a parallelogram, with two longer and two shorter length sides. As all rhombuses are indeed parallelograms, this is also a correct answer.

The quadrilateral drawn is both a parallelogram and a rhombus.

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