Pythagoras' Theorem: Finding Missing Sides in 2D Triangles
Master Pythagoras' theorem for IB MYP Maths Year 5. Learn a²+b²=c², find missing sides in 2D triangles, and avoid common errors in MYP assessments.
The Theorem
Pythagoras' theorem states that in any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse.
What You Will Use It For
- Finding the length of the hypotenuse when both shorter sides are known
- Finding a shorter side when the hypotenuse and one other side are given
- Confirming whether a triangle is right-angled (the converse of the theorem)
Step-by-Step Approach
- Identify the hypotenuse — the side opposite the right angle.
- Substitute the known values into a² + b² = c².
- Rearrange if you are solving for a shorter side: a² = c² − b².
- Square-root both sides and round appropriately.
2D Contexts You Will Encounter
MYP questions embed Pythagoras in real-world 2D settings: ladders against walls, diagonal paths across rectangles, distances between coordinate points, and cross-sections of shapes. The triangle is not always drawn explicitly — part of the skill is spotting the right angle.
Common Mistakes
- Adding when you should subtract (confusing which side is the hypotenuse)
- Forgetting to take the square root at the final step
- Rounding intermediate values, which introduces errors in the final answer
Scope Note
This topic covers 2D Pythagoras only. Three-dimensional problems — such as finding the space diagonal of a cuboid — are part of the Extended pathway (Further Pythagoras' Theorem).