Checking and further securing understanding of Pythagoras' theorem | Maths

Starter quiz

$14^2=$ ______

'196' ✓
Izzy has used her calculator to find the square root of 648. Which of these are correct for the given degree of accuracy?

25.4 (truncated to 1 decimal place) ✓

30 (nearest whole number)

25.5 (3 significant figures) ✓

25.4 (1 decimal place)

0.456 (3 decimal places)
What type of triangle is this?

scalene triangle

isosceles triangle

equilateral triangle

right-angled scalene triangle ✓

right-angled isosceles triangle
If a square has an edge length of 19 cm, then its area is ______ $\text{ cm}^2$ .

4.4

38

76

361 ✓
A square has an area of 1024 $\text{ cm}^2$ . What is the edge length of the square?

'32 cm' ✓
A square has an area of 1369 $\text{ m}^2$ . What is the perimeter of this square?

'148 m' ✓

The hypotenuse is the __________ edge of a right-angled triangle and is always opposite the right angle.

shortest

longest ✓
Match the squares with the correct area.

a

⇔

$169\text{ cm}^2$ ✓

b

⇔

$25\text{ cm}^2$ ✓

c

⇔

$144\text{ cm}^2$ ✓
Given that 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 its longest side (the hypotenuse), a = ...

64

161

225

289 ✓
Pythagoras' theorem as a formula is $c^2=a^2+b^2$ , where $c$ is the hypotenuse. Which of the following are correct rearrangements of the formula?

$a^2=b^2+c^2$

$b^2=a^2+c^2$

$a^2=c^2-b^2$ ✓

$c=\sqrt{a^2+b^2}$ ✓

$c=a+b$
Work out the length of $x$ .

'37' ✓
Work out the length of $x$ .

'20' ✓

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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
The difference between the squares of the longest and known shorter sides is the square of the remaining side
A calculator can perform these calculations efficiently
Rounding gives a less accurate answer so there might be times you wish to leave your answer with an operator

Misidentifying the hypotenuse.

The hypotenuse is the longest side of a right-angled triangle. It is always opposite the right-angle.

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.