By the end of this section you should be able to: ● understand Pythagoras’s theorem and its converse ● use Pythagoras’s theorem to fi nd unknown sides ● use Pythagoras’s theorem to prove that a given triangle is right-angled
Discuss and discover
Investigate the relationship between the sides of a right-angled triangle:
(i) Working with a classmate, draw the right-angled triangle on the right.
(ii) Square the value on each of the sides. (iii) Add the squares of the two smaller sides.
(iv) Compare the sum of the squares to the square of the longest side. What do you notice?
5 cm 4 cm
(v) Draw another two right-angled triangles, measure the lengths of each of the sides and repeat steps (ii) to (iv) for each triangle.
(vi) What can you conclude about the sides of a right-angled triangle?
Theorem 14: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
This theorem shows a relationship between the sides of a right-angled triangle. It states that if we were to form squares from each side of the triangle, then the biggest square has the exact same area as the other two squares added together.
This is called Pythagoras’s theorem and it can be written in one short equation:
c2 = a2 + b2
where c is the hypotenuse (the longest side of the triangle) and a and b are the other two sides.
c: hypotenuse
hypotenuse = c
90° a
Pythagoras’s theorem is in the formulae and tables booklet. We will look at the proof of Pythagoras’s theorem in Section C, Unit 34.