P4 Rectangles and Squares

A rectangle has four right angles and opposite sides that are equal and parallel. A square has four equal sides and four right angles. Side lengths belong to the named shape, so use the labels rather than judging a picture by eye.

Parents: ask your child to say which properties are shared before asking whether a shape is a square.

By the end you will be able to use rectangle and square properties and draw each shape with a ruler and set square.

Rectangle properties

Use this labelled non-square rectangle: length 12 cm and width 6 cm. All four angles are right angles. The two 12 cm sides are opposite and equal; the two 6 cm sides are opposite and equal. Opposite sides are parallel, while adjacent sides need not be equal.

Read the labelled rectangle

$$AB=CD=12\,\text{ cm}$$

$$BC=DA=6\,\text{ cm}$$

$$\text{all four angles are right angles}$$

Square properties and inclusion

A square has side 8 cm in the separate example below. Its four sides are equal and its four angles are right angles.

Every square is a rectangle because it has four right angles. A rectangle may be a square; when an unequal example is intended, say “non-square rectangle” or “rectangle with unequal adjacent side lengths.”

Do not use diagonal properties for this P4 lesson. The useful checks here are side lengths, right angles and parallel opposite sides.

Read the labelled square

$$AB=BC=CD=DA=8\,\text{ cm}$$

$$\text{all four angles are right angles}$$

$$\text{a square is also a rectangle}$$

Draw with a ruler and set square

To draw a 12 cm by 6 cm rectangle, draw AB = 12 cm with a ruler. Put one straight edge of the set square along AB and draw a perpendicular ray at A; repeat at B. Mark AD = 6 cm and BC = 6 cm, join C to D with the ruler, then check closure and the four right angles.

To draw an 8 cm square, draw AB = 8 cm. Use the set square at A and B to erect perpendicular rays, mark AD = 8 cm and BC = 8 cm, then join C to D. Check all four sides are 8 cm and all four corners are right angles.

🔬

Rectangle and square construction lab

🤔 Predict first: Which tool should erect the right angle at each endpoint of the first side?

A set squareA tally chartA paint brush

🔬

Area and perimeter grid lab

🤔 Predict first: A 5 by 3 grid has how many square units inside?

81516

Text alternative: the construction uses one measured first side, a set square at both endpoints to make two perpendicular rays, matching length marks and a final ruler line joining the marks. A shape is accepted after the side lengths and right-angle corners are checked.

Practise with worked steps

Practice givens 1: A shape has four right angles, opposite sides 12 cm and opposite sides 6 cm. Classify the shape as a square or a non-square rectangle.

Reveal solution: Practice 1

Given four right angles, opposite sides 12 cm and opposite sides 6 cm, it is a non-square rectangle. Its adjacent side lengths are unequal, so it is not a square.

Classify from the givens

$$\text{four right angles}+\text{equal opposite sides}\Rightarrow\text{rectangle}$$

$$12\,\text{ cm}\ne6\,\text{ cm}\Rightarrow\text{non-square}$$

Practice givens 2: Construct an 8 cm square: first side AB = 8 cm; use a set square for right angles, mark 8 cm on both perpendiculars, and join the final side.

Reveal solution: Practice 2

Given first side AB = 8 cm: draw AB, use a set square to erect a right angle at A and B, mark 8 cm on both rays, join the marks with a ruler and check all four sides. The result is an 8 cm square, which is also a rectangle.

Construct the square

$$AB=8\,\text{ cm}$$

$$AD=BC=8\,\text{ cm}$$

$$AB=BC=CD=DA\text{ and four right angles}\Rightarrow\text{square}$$

Practice givens 3: Proposed side lengths are 10 cm, 4 cm, 10 cm and 4 cm, with four right angles. Classify the shape.

Reveal solution: Practice 3

Given side lengths 10 cm, 4 cm, 10 cm, 4 cm and four right angles, opposite sides match and every angle is right. It is a non-square rectangle because adjacent sides are 10 cm and 4 cm.

Property check

$$10\,\text{ cm}=10\,\text{ cm}$$

$$4\,\text{ cm}=4\,\text{ cm}$$

$$\text{adjacent lengths differ, so the rectangle is non-square}$$

Watch out

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. A rectangle has length 12 cm and width 6 cm. Which property must it have?

   Four sides of 6 cmNo equal opposite sidesFour right angles

2. A square has side 8 cm. What is true?

   Only two sides are equalIt has no right anglesAll four sides are 8 cm

3. Which statement describes the relationship between a square and a rectangle?

   No square is a rectangleA square has no right anglesEvery square is a rectangle

4. Which tool sequence constructs the sides of a 12 cm by 6 cm rectangle?

   Use a ruler for lengths and a set square for perpendicularsUse a tally chart for all four sidesUse a protractor to measure every side

5. To draw a 12 cm by 6 cm rectangle, what should be marked on each perpendicular ray?

   12 cm18 cm6 cm

6. A rectangle has adjacent sides 10 cm and 4 cm. How should it be described?

   A square onlyA triangleA non-square rectangle

See my score