- Year 9
Length of the hypotenuse
I can use Pythagoras' theorem to find the length of the hypotenuse.
- Year 9
Length of the hypotenuse
I can use Pythagoras' theorem to find the length of the hypotenuse.
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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 calculator can perform these calculations efficiently.
- Priority of operations makes the order clear.
Keywords
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).
Hypotenuse - A hypotenuse is the side of the right-angled triangle which is opposite the right-angle.
Right-angled triangle - A right-angled triangle has exactly one 90° interior angle.
Common misconception
Pythagorean triples can be a trio of any rational numbers that, when constructed into a triangle, always produces a right-angled triangle.
Pythagorean triples are conventionally a trio of integer side lengths of a right-angled triangle, such as the 3, 4, 5 triangle. Other, similar triangles can be generated from Pythagorean triples, whose side lengths are rational, such as 0.3, 0.4, 0.5
To help you plan your year 9 maths lesson on: Length of the hypotenuse, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Length of the hypotenuse, 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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The assessment exit quiz will test your pupils' understanding of the key learning points.
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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.Which of these sides is a hypotenuse?

Q2.The triangle formed from these three squares is right-angled. What is the value of $$n$$, where $$n$$ units² is the area of a square.

Q3.If three squares with different areas are joined at their vertices, what type of triangle would be formed?
Q4.Angle $$a°$$ is an acute angle, but is the largest angle in this triangle. Which of these are possible values of $$t$$, where $$t$$ units² is the area of a square.

Q5.Which of these are true for the Pythagoras' theorem?
Q6.A right-angled triangle is formed from three squares. The area of two of the squares are 75 units² and 25 units². What are the possible areas of the third square?
Assessment exit quiz
6 Questions
Q1.The length of the hypotenuse for this right-angled triangle is cm.

Q2.$$k$$ cm² is the area of the square from the hypotenuse of the triangle. The value of $$k$$ is .

Q3.Calculate the length of the hypotenuse of this triangle, in units.

Q4.The area, $$w$$, of the largest square in this diagram is cm².

Q5.Calculate the length of the hypotenuse for this triangle. (Give your answer to 1 d.p.).

Q6.The length of the hypotenuse of this triangle, rounded to 1 d.p. is cm.
