Pythagoras Theorem
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides: a^2 + b^2 = c^2.
What You Need to Know
Key Concept Diagram
The hypotenuse is the longest side of a right-angled triangle, opposite the right angle
Pythagoras' theorem: a^2 + b^2 = c^2 where c is the hypotenuse
To find the hypotenuse: c = sqrt(a^2 + b^2)
To find a shorter side: a = sqrt(c^2 - b^2)
Pythagorean triples are whole-number solutions: 3-4-5, 5-12-13, 8-15-17
Key Vocabulary
Hypotenuse
The longest side of a right-angled triangle; it is always opposite the right angle
Right Angle
An angle of exactly 90 degrees, shown by a small square in diagrams
Pythagorean Triple
A set of three whole numbers that satisfy a^2 + b^2 = c^2 (e.g. 3, 4, 5)
Square Root
The inverse of squaring; used to find side lengths from the theorem
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A right-angled triangle has legs of 3 cm and 4 cm. What is the length of the hypotenuse?
Question 2
A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the other leg?
Question 3
Which set of numbers is a Pythagorean triple?
Key Concepts Summary
- ●The hypotenuse is the longest side of a right-angled triangle, opposite the right angle
- ●Pythagoras' theorem: a^2 + b^2 = c^2 where c is the hypotenuse
- ●To find the hypotenuse: c = sqrt(a^2 + b^2)
- ●To find a shorter side: a = sqrt(c^2 - b^2)
- ●Pythagorean triples are whole-number solutions: 3-4-5, 5-12-13, 8-15-17