New
New
Year 10
Foundation

Using Pythagoras' theorem to justify a right-angled triangle

I can use Pythagoras' theorem to justify whether a triangle is right-angled.

New
New
Year 10
Foundation

Using Pythagoras' theorem to justify a right-angled triangle

I can use Pythagoras' theorem to justify whether a triangle is right-angled.

Lesson details

Key learning points

  1. For a triangle to be right-angled, Pythagoras' theorem must hold
  2. By substituting in the three lengths, you can show whether the theorem holds
  3. If the numbers produce a true statement, the triangle is right-angled
  4. If they do not produce a true statement, the triangle is not right-angled

Common misconception

Incorrectly rearranging Pythagoras' theorem.

It can be helpful to scaffold the steps for any pupils who are struggling with rearranging.

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.

You may wish to have your pupils investigate the level of accuracy in using rounded values in their calculations in the second learning cycle.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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.
scalene
isosceles
equilateral
Correct answer: right-angled
obtuse-angled
Q2.
Put the stages of working in order.
An image in a quiz
1 - $$x^2=8^2+15^2$$
2 - $$x^2=64+225$$
3 - $$x^2=289$$
4 - $$x=\sqrt{289}$$
5 - $$x=17$$
6 - The hypotenuse is 17 cm.
Q3.
Work out the length of the hypotenuse.
An image in a quiz
Correct Answer: 26 cm, 26, twenty six
Q4.
Work out the length of $$x$$.
An image in a quiz
Correct Answer: 6 cm, 6, six
Q5.
Select the correct answers for $$x$$.
An image in a quiz
Correct answer: $$\sqrt{87}$$ cm
Correct answer: 9.3 cm (rounded to the nearest tenth)
9.32 cm (rounded to 3 significant figures)
Correct answer: 9.32 cm (truncated to 2 decimal places)
9.32738 (rounded to 5 significant figures)
Q6.
A trapezium is formed by a right-angled triangle and a rectangle. Work out the length of the edge marked $$x$$.
An image in a quiz
Correct Answer: 29 cm, twenty nine, 29

6 Questions

Q1.
If a triangle is right-angled this means...
Correct answer: ...one of the angles is $$90^\circ$$.
Correct answer: ...the longest edge is called the hypotenuse.
…there are three different angles.
Correct answer: ...Pythagoras' theorem holds.
...the other two angles are $$45^\circ$$.
Q2.
If a triangle is right-angled then $$a^2+b^2=c^2$$ where...
...$$a$$ is the hypotenuse.
...$$b$$ is the hypotenuse.
Correct answer: ...$$c$$ is the hypotenuse.
Q3.
A triangle has these three edge lengths: 13 cm, 18cm and 31 cm. Is it a right-angled triangle?
Yes, as 13 + 18 = 31.
Correct answer: No, as $$13^2+18^2\neq 31^2$$.
Impossible to tell, as we haven't got a diagram.
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?
No, you cannot have a right-angled isosceles triangle.
Correct answer: Yes, as Pythagoras' theorem holds.
Impossible to tell, as isosceles triangles can have many different angles.
Q5.
Here is a plan view of a room. There are two external walls; are they perpendicular?
An image in a quiz
Yes - Pythagoras' theorem holds.
Correct answer: No - Pythagoras' theorem does not hold.
There is not enough information.
Q6.
Which of these triangles ABC, are right-angled?
AB = 7 cm, AC = 9 cm, BC = 16 cm
Correct answer: AB = 6 cm, AC = 8 cm, BC = 10 cm
AB = 8 cm, AC = 14 cm, BC = 22 cm
Correct answer: AB = 20 cm, AC = 99 cm, BC = 101 cm
Correct answer: AB = 40 cm, AC = 198 cm, BC = 202 cm