4.10

Pythagoras theorem

9 flashcards to master Pythagoras theorem

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Definition Flip

State Pythagoras' Theorem for a right-angled triangle with sides a, b, and hypotenuse c.

Answer Flip

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.

Key Concept Flip

Identify the hypotenuse in a right-angled triangle.

Answer Flip

The hypotenuse is always the longest side of a right-angled triangle. It is located opposite the right angle (90°).

Key Concept Flip

A right-angled triangle has sides of length 3 cm and 4 cm. Calculate the length of the hypotenuse.

Answer Flip

Using Pythagoras' Theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 cm.

Key Concept Flip

If the hypotenuse of a right-angled triangle is 13 cm and one side is 5 cm, find the length of the other side.

Answer Flip

Using Pythagoras' Theorem: a² + b² = c² so b² = c² - a² = 13² - 5² = 169 - 25 = 144. Therefore, b = √144 = 12 cm.

Key Concept Flip

Describe how Pythagoras' Theorem is used to find the shortest distance between two points on a 2D plane.

Answer Flip

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.

Definition Flip

Explain what a Pythagorean triple is, and give an example.

Answer Flip

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).

Key Concept Flip

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?

Answer Flip

Using Pythagoras' Theorem: height² = ladder² - distance². height² = 6² - 2² = 36 - 4 = 32. Therefore, height = √32 ≈ 5.66m.

Key Concept Flip

How can you test if a triangle with sides of length 7 cm, 24 cm, and 25 cm is a right-angled triangle?

Answer Flip

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.

Key Concept Flip

A ship sails 7 km East and then 24 km North. How far is it from its starting point?

Answer Flip

This forms a right-angled triangle. Distance from start = √(7² + 24²) = √(49 + 576) = √625 = 25 km.

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4.9 Constructions and loci 5.1 Perimeter and area

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).

About Pythagoras theorem (4.10)

These 9 flashcards cover everything you need to know about Pythagoras theorem for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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