Study Notes
Pythagoras' Theorem is a fundamental principle in geometry that applies to right-angled triangles. It states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Hypotenuse — the longest side of a right-angled triangle, opposite the right angle. Example: In a triangle with sides 3, 4, and 5, the hypotenuse is 5.
- Right-angled triangle — a triangle with one angle measuring 90 degrees. Example: A triangle with angles 90°, 45°, and 45°.
- Pythagorean triple — a set of three positive integers a, b, and c that fit the rule a² + b² = c². Example: The numbers 3, 4, and 5 form a Pythagorean triple.
Exam Tips
Key Definitions to Remember
- Pythagoras' Theorem: a² + b² = c²
- Hypotenuse: the longest side of a right-angled triangle
Common Confusions
- Confusing which side is the hypotenuse
- Forgetting to square the sides before adding
Typical Exam Questions
- What is the length of the hypotenuse if the other sides are 6 and 8? Answer: 10
- If one side of a right-angled triangle is 5 and the hypotenuse is 13, what is the length of the other side? Answer: 12
- How do you verify if a triangle with sides 7, 24, and 25 is a right-angled triangle? Answer: Check if 7² + 24² = 25²
What Examiners Usually Test
- Ability to apply Pythagoras' Theorem to find missing sides
- Understanding of which side is the hypotenuse in a triangle