Checking and securing understanding of Pythagoras' theorem | Maths

Starter quiz

Which of the following statements is true for these triangles?
- The triangles are similar. ✓
- The triangles are not similar.
- It is not possible to know whether the triangles are similar or not.
Which of these statements is true?
- Isosceles triangles are always similar to each other.
- Equilateral triangles are always similar to each other. ✓
- Right triangles are always similar to each other.
- Scalene triangles are always similar to each other.
What is the value of n?
- '21' ✓
Which of these statements is true?
- Rectangles are always similar to each other.
- Parallelograms are always similar to each other.
- Rhombi are always similar to each other.
- Squares are always similar to each other. ✓
What is the value of n?
- '158ᵒ' ✓
An isosceles triangle has an internal angle of 100ᵒ, what are the other two angles?
- 100ᵒ, 80ᵒ
- 40ᵒ, 40ᵒ ✓
- 60ᵒ, 60ᵒ

Exit quiz

In a right triangle, if the shortest sides are 6 cm and 8 cm, what is the length of the hypotenuse?
- 10cm ✓
- 12cm
- 8cm
$a^2+b^2=c^2$ is a formula for which type of triangle?
- scalene
- isosceles
- right angled ✓
- equilateral
Which formula below is a rearrangement of $a^2+b^2=c^2$ ?
- $a^2+c^2=b^2$
- $a^2-c^2=b^2$
- $c^2-a^2=b^2$ ✓
In a right triangle, if the hypotenuse is 40 cm and a second side is 24 cm, what is the length of the third side? (Use a calculator to help you.)
- 32 cm ✓
- 30 cm
- 34 cm
In a right triangle, if the hypotenuse is 30 cm and a second side is 24 cm, what is the area? (Use a calculator to help you.)
- $216 cm^2$ ✓
- $210 cm^2$
- $206 cm^2$
In a right triangle, if the hypotenuse is 65 cm and a second side is 60 cm, what is the perimeter? (Use a calculator to help you.)
- 150 cm ✓
- 170 cm
- 140 cm

Worksheet

Presentation

Video

Lesson Details

Key learning points

The sum of the squares of the two shorter sides equals the square of the longest side.
The longest side is always opposite the right angle.
a^2+b^2=c^2 can be rearranged to find one of the shorter side lengths.
If the right-angled triangle is not immediately available, see if you can construct one.

Common misconception

Pupils may find it initially difficult to see how Pythagoras' theorem can be used when a right-angled triangle is not immediately available.

Encourage pupils to draw their own diagram in cases where there is not one provided. In cases where pairs of coordinates are being used, encourage pupils to draw on horizontal and vertical line segments.

Keywords

Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.