Myths about teaching can hold you back
- Year 9
Determining which side
I can identify which side length is missing and use the appropriate form of Pythagoras' theorem to calculate it.
- Year 9
Determining which side
I can identify which side length is missing and use the appropriate form of Pythagoras' theorem to calculate it.
Lesson details
Key learning points
- The hypotenuse is the side opposite the right angle.
- It does not matter which of the shorter sides is identified as a or b.
Keywords
Right-angled triangle - A right-angled triangle has exactly one 90° interior angle.
Hypotenuse - A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.
Pythagoras’ theorem - Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).
Common misconception
I can only use Pythagoras' theorem to find the length of a side of a right-angled triangle when the right-angle marker is labelled, so I know which side is the hypotenuse.
The right-angle marker doesn't need to be explicitly labelled in order to be able to identify the right-angle. You can use knowledge of "interior angles in a triangle sum to 180°" to find the right angle, given two other angles.
To help you plan your year 9 maths lesson on: Determining which side, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Determining which side, 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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.In this diagram, $$a$$ cm² = 140 cm² and $$b$$ cm² = 185 cm².
The area $$c$$ cm² is cm².

Q2.In this diagram, $$b$$ cm² = 77 cm² and $$c$$ cm² = 107 cm².
Find the area $$a$$ cm².

Q3.In the diagram, $$a$$ = 1504 and $$b$$ = 1200.
Find the length of the hypotenuse of the triangle.

Q4.In this diagram, $$a$$ = 49, $$b$$ = 576, and $$c$$ = 625.
The perimeter of the triangle is cm.

Q5.In a right-angled triangle, one of its acute interior angles is 33°. What is the size of its other acute interior angle?
Q6.The size of an acute angle in a right-angled isosceles triangle is °.
Assessment exit quiz
6 Questions
Q1.Which of these triangles are right-angled triangles?

Q2.In the diagram, $$x$$ = 101, $$y$$ = 45, $$z$$ = 56.
Which of these angles is the right angle?

Q3.A right-angled triangle has sides of length 21 inches, 220 inches, and 221 inches.
Which of these are correct Pythagoras' theorem equations for this triangle?
Q4.A right-angled triangle has sides of length 39 inches, 80 inches, and 89 inches.
Which of these are correctly rearranged Pythagoras' theorem equations for this triangle?
Q5.Using Pythagoras' theorem, calculate the length of the side labelled $$j$$, rounded to 1 decimal place. Length of side $$j$$ is cm.

Q6.Using Pythagoras' theorem twice, calculate the length of the side labelled $$h$$, rounded to 2 decimal places. Length of side $$h$$ is cm.
