Summary
Pythagoras' Theorem is used to find the length of a side in a right-angled triangle. It states that 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.
- Pythagorean Triple — a set of three positive integers that fit the Pythagorean theorem. Example: (3, 4, 5) is a Pythagorean triple.
- Right-angled Triangle — a triangle with one angle measuring 90 degrees. Example: A triangle with angles 90°, 45°, and 45° is a right-angled triangle.
Exam Tips
Key Definitions to Remember
- The hypotenuse is the longest side of a right-angled triangle.
- Pythagoras' Theorem: a² + b² = c², where c is the hypotenuse.
Common Confusions
- Confusing the hypotenuse with one of the other sides.
- Forgetting to take the square root when solving for a side length.
Typical Exam Questions
- What is the length of the hypotenuse if the other two 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 side lengths.
- Understanding of the relationship between the sides of a right-angled triangle.