Myths about teaching can hold you back
- Year 9
Problem solving with similarity and Pythagoras' theorem
I can use my knowledge of similarity and Pythagoras' theorem to solve problems.
- Year 9
Problem solving with similarity and Pythagoras' theorem
I can use my knowledge of similarity and Pythagoras' theorem to solve problems.
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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.
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.
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.
To help you plan your year 9 maths lesson on: Problem solving with similarity and Pythagoras' theorem, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Problem solving with similarity and Pythagoras' theorem, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Geometrical properties: similarity and Pythagoras' theorem unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Equipment
Licence
Prior knowledge starter quiz
6 Questions
Q1.Alex rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?

Q2.The perimeter of this right-angled triangle is cm.

Q3.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.

Q4.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.
Q5.These two triangles are similar to each other. The side marked $$u$$ cm is cm long.

Q6.An isosceles triangle has an angle of 22°. Which of these are possible sizes of one of the other angles?
Assessment exit quiz
6 Questions
Q1.These two triangles are similar to each other and are both in the same orientation. The length of the hypotenuse marked $$h$$ is cm.

Q2.The area of this triangle is cm².

Q3.Which of these statements are correct for this triangle?

Q4.Which of these statements are correct for this triangle?

Q5.Each square is 1 unit in length. The shortest distance from point A to point B is units (rounded to 2 d.p.).

Q6.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).
