Geometry and Properties

1. (a) All four shapes — the square, rectangle, rhombus, and trapezoid — are quadrilaterals. A quadrilateral is any closed shape with exactly $4$ sides and $4$ angles. Each of these shapes meets that definition.

(b) Yes, a square is also a rectangle. A rectangle is any shape with $4$ sides and $4$ right angles. A square has $4$ right angles, so it qualifies.

Yes, a square is also a rhombus. A rhombus is any shape with $4$ equal sides. A square has $4$ equal sides, so it qualifies.

A square is a special shape that is both a rectangle AND a rhombus.

2. (a) The shape is a rectangle. It has $4$ right angles and two pairs of sides with different lengths.

(b) Yes, it is a quadrilateral because it has exactly $4$ sides and $4$ angles.

3. (a) The pizza is cut into $4$ equal slices, so each slice is:

$\frac{1}{4}$

of the whole pizza.

(b) Eating $2$ out of $4$ equal slices means you ate:

$\frac{2}{4}$

of the pizza.

(c) There are $4 - 2 = 2$ slices left, so the fraction remaining is:

$\frac{2}{4}$

of the pizza (which is the same as $\frac{1}{2}$).

4. (a) The rectangle is split into $6$ equal parts, so each part is:

$\frac{1}{6}$

of the whole rectangle.

(b) Shading $3$ out of $6$ parts means the shaded fraction is:

$\frac{3}{6}$

(c) $\frac{3}{6}$ is equal to $\frac{1}{2}$, because $3$ is half of $6$. So:

$\frac{3}{6} = \frac{1}{2}$

5. (a) Maya is correct. A square is always a rhombus because a rhombus is defined as a shape with $4$ equal sides, and a square has $4$ equal sides.

Leo is incorrect. While not every rhombus is a square, it is not true that a rhombus can never be a square. A square is a special kind of rhombus — one that also has $4$ right angles.

(b) Imagine a diamond shape where all $4$ sides are the same length, but the angles are not $90°$ — two angles are wide (obtuse) and two are narrow (acute). This is a rhombus that is NOT a square, because it lacks right angles.