Determine whether this statement is true or false. All rhombuses are parallelograms.
To decide whether the statement is true or false, we need to know what the two types of shape in this statement mean. What is a rhombus? And what is a parallelogram?
Let’s remind ourselves what a parallelogram is to begin with. Well, there’s a big clue in the name. A parallelogram is a quadrilateral or a four-sided shape with two pairs of parallel sides. For example, this shape has two pairs of parallel sides. This pair of sides is parallel and this pair of sides is parallel too. Two pairs of parallel sides.
Rectangles have two pairs of parallel sides, so we can say that rectangles are a type of parallelogram. And the opposite sides on a square are parallel too. A square is a type of parallelogram.
Our question asks us about rhombuses. Are all rhombuses parallelograms? What’s a rhombus? A rhombus is a type of quadrilateral with opposite sides that are parallel and all sides equal. Here are some examples of rhombuses. We can see that they’re all quadrilaterals. In other words, they’ve all got four sides They’ve also each got opposite sides that are parallel. The other thing we notice about rhombuses is that all the sides are the same length.
Let’s turn our fact about parallelograms into a checklist. Are all rhombuses quadrilaterals? Yes, they all have four sides. Do all rhombuses have two pairs of parallel sides? Yes. And so we can say all rhombuses are parallelograms. They’re a special type of parallelogram where all the sides are equal. The statement is true.