Generalising: Pythagoras's theorem
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Lesson details
Key learning points
- In this lesson, we will develop an understanding of Pythagoras' theorem by drawing upon our tilted squares knowledge.
Licence
This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.
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6 Questions
Q1.
Look at the diagram below and fill in the gap: The area of the larger square is equal to the ........... of the area of the two smaller squares.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707167293%2Fh2obq5n8kju9qnq3kwvx.png&w=1080&q=75)
difference
product
Q2.
What is the side length of the larger square?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707167316%2Fknqwjpwz0cylfg9wvosx.png&w=828&q=75)
√8
10
8
Q3.
What is the side length of the larger square?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707167318%2Fs74zljiyve1olohpa1mm.png&w=828&q=75)
√12
12
26
Q4.
What is the side length of the larger square?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707167325%2Ffhgy8xjiwkr7fpij5izj.png&w=828&q=75)
√7
29
7
Q5.
If the pink triangle has a base of 10 and a height of 2. What is the area of the green tilted square?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707167333%2Funqhzrghuelwwcci5jyw.png&w=640&q=75)
√104
√20
20
Q6.
If the pink triangle has a base of 10 and a height of 2. What is the side length of the green square?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707167337%2Fbpxzftbvplokhig2tnfm.png&w=640&q=75)
√29
104
29
4 Questions
Q1.
What is the name of the longest side of a right-angled triangle?
base
height
Q2.
Which diagram shows the hypotenuse correctly highlighted and labelled?
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707212365%2Fhtip0aemsgkwv3oqzpkm.png&w=640&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707138194%2Fyapj3ulqhpclbn4r77vz.png&w=640&q=75)
Option 1
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707199424%2Fi724mnhp3xssvmmjwjlw.png&w=640&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707201632%2Fhtdvs1fv75pgtlclxkzm.png&w=640&q=75)
Option 3
Q3.
A right-angled triangle has the sides a, b and c. Choose the correct formula for finding the length of side a.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707171397%2Ffgpzuxat61s7wwsy2zgg.png&w=640&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707138214%2Fjuebmmyx0jxpo5pkdlav.png&w=828&q=75)
Option 1
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707139440%2Frgkt8x0kku2lpvetunim.png&w=640&q=75)
Option 2
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707140434%2Fkdje7m6w55ozdu0lcmce.png&w=750&q=75)
![](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707141100%2Fv0a8j9jx9ramwcp3zr9q.png&w=750&q=75)
Option 4
Q4.
Work out the length of the hypotenuse of the triangle shown below.
![An image in a quiz](/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707171401%2Feaxuuuffhm9zkqdwv8c3.png&w=640&q=75)
14 cm
25 cm
7 cm