Investigate the shapes made when rectangles are cut on the diagonal | Maths

Starter quiz

Which of these shapes are rectangles?

a ✓

b ✓

c

d ✓
Which of these shapes are squares?

a

b ✓

c

d ✓
Why is this shape not a rectangle?

It does not have 4 straight sides.

It does not have any sides of equal length.

It does not have 4 right angles. ✓

It is not a quadrilateral.
Match the description to the type of shape.

Rectangle

⇔

A four-sided polygon with 4 right angles. ✓

Quadrilateral

⇔

Any four-sided polygon. ✓

Square

⇔

A four-sided polygon with 4 right angles and 4 equal sides. ✓
5. Match each line to the correct name.

a

⇔

diagonal ✓

b

⇔

vertical ✓

c

⇔

horizontal ✓
Look at this pattern. How many rectangles are there altogether?

'9' ✓

Exit quiz

Aisha cuts this rectangle in half using a vertical line. What shape will both halves be?

Squares

Rectangles ✓

Triangles
Aisha cuts this rectangle in half using a diagonal line. What shapes will both halves be?

Squares

Rectangles

Triangles ✓
Aisha cuts this square into two triangles using one diagonal line. Which of these statements is true?

Both triangles have one right angle. ✓

One triangle is larger than the other.

Both triangles have two sides of equal length. ✓
Laura uses two diagonal lines, cutting from each vertex at the top of the square to each at the bottom. How many triangles would the rectangle be cut up into?

'4' ✓
Aisha cuts a rectangle into four triangles. This is one of the triangles. How many angles inside the shape are smaller than a right angle?

'2' ✓
Which statements are always true? When you make two diagonal cuts through any rectangle…

…each triangle will have at least two sides the same length. ✓

…all of the triangles are identical.

…you always end up with four triangles. ✓

…all of the triangles will have right angles.

Worksheet

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Video

Lesson Details

Key learning points

An angle can be exactly a right angle.
An angle can be less than or greater than a right angle.
When you cut a square using two diagonal lines, you get four identical triangles.
When you cut a rectangle that is not a square using two diagonal lines, you get two pairs of identical triangles.

Common misconception

Pupils may find it hard to recognise when an angle is greater than a right angle.

You can model this by trying to move the obtuse angle (though pupils don't need to know the term yet) within a right angle checker. They should be able to see that it is too large to fit.

Keywords

Diagonal - A straight line connecting one vertex to another, but is not the side or edge.