Squares, Rectangles, and Rhombuses

Mathematics · Geometry · ages 8-9

Name ______________________ Date ____________

Which statement is true about every square?
- It has four equal sides and four right angles
- It has four equal sides, but the angles can be any size
- It has four right angles, but the sides can be different lengths
What is a quadrilateral?
- A shape with exactly four straight sides
- A shape with exactly three straight sides
- A shape where all sides must be equal
A square is also a rectangle.
Circle one: True False
A shape has four equal sides, but its angles are not right angles. What is it?
- A rhombus that is not a square
- A square
- A rectangle
Zara draws a shape with four right angles, but two sides are longer than the other two. What did she draw?
- A rectangle that is not a square
- A square
- A rhombus
Every rhombus is a rectangle.
Circle one: True False
Maya says, if a shape is a rhombus, it must be a square. What is wrong with her thinking?
- A rhombus needs equal sides but not right angles, so it is not always a square
- A rhombus is never a square
- A square does not need equal sides
Leo sorts shapes into a Venn diagram with circles for quadrilaterals, rectangles, and squares. Where should he place a shape with four sides of different lengths and no right angles?
- Inside the quadrilateral circle only
- Inside the rectangle circle
- Inside the square circle

Answer key

For grown-ups. Fold this page away before handing over the rest.

It has four equal sides and four right angles · A square always has both features: four matching sides and four right angles.
A shape with exactly four straight sides · Quadrilateral just means four-sided shape. Squares, rectangles, and rhombuses are all types of quadrilaterals.
True · A square has four right angles, so it meets every rule a rectangle needs.
A rhombus that is not a square · Equal sides make it a rhombus. Since the angles are not right angles, it is not a square.
A rectangle that is not a square · It has four right angles, so it is a rectangle. Since the sides are not all equal, it cannot be a square too.
False · A rhombus only needs equal sides. Unless its angles are also right angles, it is not a rectangle.
A rhombus needs equal sides but not right angles, so it is not always a square · Squares are special rhombuses, but a rhombus only becomes a square when it also picks up the right-angle rule.
Inside the quadrilateral circle only · It has four straight sides, so it belongs in the quadrilateral circle. It skips the rectangle and square rules, so it stays outside those smaller circles.