Study Notes
Pythagoras Theorem is a fundamental principle in geometry that applies to right-angled triangles. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Right-angled triangle — a triangle with one angle equal to 90 degrees Example: A triangle with angles 90°, 45°, and 45°.
- Hypotenuse — the side opposite the right angle in a right-angled triangle Example: In a triangle with sides 3, 4, and 5, the hypotenuse is 5.
- Pythagorean theorem — in a right-angled triangle, c² = a² + b², where c is the hypotenuse Example: For a triangle with sides 3, 4, and 5, 5² = 3² + 4².
Exam Tips
Key Definitions to Remember
- Right-angled triangle: A triangle with one 90-degree angle.
- Hypotenuse: The longest side opposite the right angle.
- Pythagorean theorem: c² = a² + b².
Common Confusions
- Confusing the hypotenuse with one of the legs.
- Forgetting to square the sides when using the theorem.
Typical Exam Questions
- What is the length of the hypotenuse if the other sides are 6 and 8? Answer: 10 (since 6² + 8² = 10²).
- How do you find the length of a missing side in a right-angled triangle? Answer: Use the Pythagorean theorem, rearranging as needed.
- Calculate the length of a side given the hypotenuse and one side. Answer: Subtract the square of the known side from the square of the hypotenuse, then take the square root.
What Examiners Usually Test
- Ability to identify right-angled triangles.
- Correct application of the Pythagorean theorem.
- Solving real-world problems using right-angled triangles.