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- Year 10•
- Higher
Using Pythagoras' theorem to justify a right-angled triangle
I can use Pythagoras' theorem to justify whether a triangle is right-angled.
- Year 10•
- Higher
Using Pythagoras' theorem to justify a right-angled triangle
I can use Pythagoras' theorem to justify whether a triangle is right-angled.
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Lesson details
Key learning points
- For a triangle to be right-angled, Pythagoras' theorem must hold
- By substituting in the three lengths, you can show whether the theorem holds
- If the numbers produce a true statement, the triangle is right-angled
- If they do not produce a true statement, the triangle is not right-angled
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.
Common misconception
Incorrectly rearranging Pythagoras' theorem.
It can be helpful to scaffold the steps for any pupils who are struggling with rearranging.
To help you plan your year 10 maths lesson on: Using Pythagoras' theorem to justify a right-angled triangle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Using Pythagoras' theorem to justify a right-angled triangle, 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.
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Explore more key stage 4 maths lessons from the Right-angled trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a __________ triangle is equal to the square of the hypotenuse.
Q2.Put the stages of working in order.
Q3.Work out the length of the hypotenuse.
Q4.Work out the length of $$x$$.
Q5.Select the correct answers for $$x$$.
Q6.A trapezium is formed by a right-angled triangle and a rectangle. Work out the length of the edge marked $$x$$.
Assessment exit quiz
6 Questions
Q1.If a triangle is right-angled this means...
Q2.If a triangle is right-angled then $$a^2+b^2=c^2$$ where...
Q3.A triangle has these three edge lengths: 13 cm, 18cm and 31 cm. Is it a right-angled triangle?
Q4.An isosceles triangle has these three edge lengths: $$19\sqrt{2}$$ cm, $$19\sqrt{2}$$ cm and 38 cm. Is it a right-angled triangle?
Q5.Here is a plan view of a room. There are two external walls; are they perpendicular?
Q6.Which of these triangles ABC, are right-angled?