Pythagoras Theorem

Study Notes

Pythagoras' Theorem is used to find the length of a side in a right-angled triangle.

• Pythagoras' Theorem — In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Example: If one side is 8 and the hypotenuse is 9, then the other side is $\sqrt{17}$ or approximately 4.12.

Exam Tips

Key Definitions to Remember

• The hypotenuse is the longest side of a right-angled triangle.
• Pythagoras' Theorem: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

Common Confusions

• Confusing which side is the hypotenuse.
• Forgetting to take the square root after finding $x^2$.

Typical Exam Questions

• What is the length of the hypotenuse if the other sides are 3 and 4? Answer: 5
• If one side is 5 and the hypotenuse is 13, what is the length of the other side? Answer: 12
• How do you find a missing side in a right-angled triangle using Pythagoras' Theorem? Answer: Use $a^2 + b^2 = c^2$ and solve for the missing side.

What Examiners Usually Test

• Ability to correctly apply Pythagoras' Theorem.
• Understanding which side is the hypotenuse.
• Correct calculation and simplification of square roots.