Pythagoras theorem
Cambridge IGCSE Mathematics (0580) · Unit 4: Geometry · 9 flashcards
Pythagoras theorem is topic 4.10 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Angles in polygons and Parallel lines. In one line: Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is a² + b² = c².
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 2 definitions, 2 key concepts and 3 application cards — covering the precise wording mark schemes reward. Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
State Pythagoras' Theorem for a right-angled triangle with sides a, b, and hypotenuse c
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is a² + b² = c².
Questions this Pythagoras theorem deck will help you answer
- › Identify the hypotenuse in a right-angled triangle.
- › Describe how Pythagoras' Theorem is used to find the shortest distance between two points on a 2D plane.
- › A ladder 6m long leans against a wall. If the foot of the ladder is 2m away from the wall, how high up the wall does the ladder reach?
- › How can you test if a triangle with sides of length 7 cm, 24 cm, and 25 cm is a right-angled triangle?
- › A ship sails 7 km East and then 24 km North. How far is it from its starting point?
State Pythagoras' Theorem for a right-angled triangle with sides a, b, and hypotenuse c.
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is a² + b² = c².
Identify the hypotenuse in a right-angled triangle.
The hypotenuse is always the longest side of a right-angled triangle. It is located opposite the right angle (90°).
A right-angled triangle has sides of length 3 cm and 4 cm. Calculate the length of the hypotenuse.
Using Pythagoras' Theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 cm.
If the hypotenuse of a right-angled triangle is 13 cm and one side is 5 cm, find the length of the other side.
Using Pythagoras' Theorem: a² + b² = c² so b² = c² - a² = 13² - 5² = 169 - 25 = 144. Therefore, b = √144 = 12 cm.
Describe how Pythagoras' Theorem is used to find the shortest distance between two points on a 2D plane.
The shortest distance is the hypotenuse of a right-angled triangle where the other sides represent the horizontal and vertical distances between the two points. Calculate the horizontal and vertical distances, then use Pythagoras' Theorem to find the hypotenuse.
Explain what a Pythagorean triple is, and give an example.
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy Pythagoras' Theorem (a² + b² = c²). A common example is (3, 4, 5) because 3² + 4² = 5² (9 + 16 = 25).
A ladder 6m long leans against a wall. If the foot of the ladder is 2m away from the wall, how high up the wall does the ladder reach?
Using Pythagoras' Theorem: height² = ladder² - distance². height² = 6² - 2² = 36 - 4 = 32. Therefore, height = √32 ≈ 5.66m.
How can you test if a triangle with sides of length 7 cm, 24 cm, and 25 cm is a right-angled triangle?
Apply Pythagoras' Theorem: if the sum of the squares of the two shorter sides equals the square of the longest side, it's a right-angled triangle. In this case, 7² + 24² = 49 + 576 = 625 = 25², so it is a right-angled triangle.
A ship sails 7 km East and then 24 km North. How far is it from its starting point?
This forms a right-angled triangle. Distance from start = √(7² + 24²) = √(49 + 576) = √625 = 25 km.
Key Questions: Pythagoras theorem
State Pythagoras' Theorem for a right-angled triangle with sides a, b, and hypotenuse c.
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is a² + b² = c².
Explain what a Pythagorean triple is, and give an example.
A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy Pythagoras' Theorem (a² + b² = c²). A common example is (3, 4, 5) because 3² + 4² = 5² (9 + 16 = 25).
More topics in Unit 4 — Geometry
Pythagoras theorem sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Pythagoras theorem deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
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