Problem solving with similarity and Pythagoras' theorem | Maths

Starter quiz

Alex rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?

The hypotenuse of the triangle is side P ✓

The hypotenuse of the triangle is side Q

The hypotenuse of the triangle is side R

Side R has length of 60 units. ✓

Side R has length of 69.64 units.
The perimeter of this right-angled triangle is ______ cm.

'182' ✓
Adhesive tape is placed along the two diagonals of this rectangular picture frame. How much adhesive tape is needed, rounded to the nearest cm? ______ cm of tape.

'186' ✓
Andeep and Sofia need to split a 3.6 metre roll of adhesive tape in the ratio 7 : 5. The length of the adhesive tape that Andeep receives is ______ centimetres.

'210' ✓
These two triangles are similar to each other. The side marked $u$ cm is ______ cm long.

'64' ✓
An isosceles triangle has an angle of 22°. Which of these are possible sizes of one of the other angles?

11°

22° ✓

45°

79° ✓

136° ✓

Exit quiz

These two triangles are similar to each other and are both in the same orientation. The length of the hypotenuse marked $h$ is ______ cm.

'40' ✓
The area of this triangle is ______cm².

'120' ✓
Which of these statements are correct for this triangle?

You need to use Pythagoras' theorem to find the size of angle $g$ .

You do not need to use Pythagoras' theorem to find the size of angle $g$ . ✓

$g$ ° = 27°

$g$ ° = 43° ✓

$g$ ° = 47°
Which of these statements are correct for this triangle?

The perimeter of this triangle is 16 + 25.4 + 19.7 = 61.1 cm (to 1 d.p.). ✓

The perimeter of this triangle is 16 + 25.4 + 25.4 = 92.4 cm (to 1 d.p.).

The area of this triangle is 158 cm² (to the nearest cm²). ✓

The area of this triangle is 203.2 cm² (to 1 d.p.).

$f°$ = 180° − 90° − 51° = 39°.
Each square is 1 unit in length. The shortest distance from point A to point B is ______ units (rounded to 2 d.p.).

'10.05' ✓
Point C is at the coordinate (12, 3). The perimeter of a triangle whose vertices are at points A, B, and C is ______ units (to the nearest unit).

'32' ✓

Worksheet

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Lesson Details

Key learning points

Right-angled triangles can be seen in real-life (e.g. ladder against a vertical wall).
A ratio table can help you find the scalar and functional multipliers in similar shapes.
It can be initially difficult to identify whether Pythagoras' theorem can be used.

Common misconception

Every question that has a right-angled triangle must use Pythagoras' theorem to be solved.

It is easy to get into a habit of using Pythagoras' theorem when learning the topic, but it is likely you have seen several maths problems in the past with right-angled triangles, which ask to find areas and angles, without using Pythagoras' theorem.

Keywords

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.