Geometry and Measurement - The Pythagorean Theorem

Grade 7IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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a

A right-angled triangle labeled with legs a and b, and hypotenuse c.

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90^{\circ}

Diagram showing the relationship between the right angle and the hypotenuse.

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(a, b, c)

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The Converse of the Pythagorean Theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled.

📐Formulae

a^2 + b^2 = c^2

c = \sqrt{a^2 + b^2}

a = \sqrt{c^2 - b^2}

b = \sqrt{c^2 - a^2}

💡Examples

Problem 1:

5\text{ cm}

Solution:

a = 5

Explanation:

To find the longest side (hypotenuse), we sum the squares of the two shorter sides and then take the square root of that sum.

Problem 2:

10\text{ m}

Solution:

c = 10

Explanation:

When the hypotenuse is already known, we must subtract the square of the known leg from the square of the hypotenuse before taking the square root.

Problem 3:

9\text{ m}

A diagram of a ladder leaning against a wall forming a right-angled triangle.

Solution:

a^2 + b^2 = c^2

Explanation:

9\text{ m}

Problem 4:

24\text{ m}

A rectangle with a diagonal shown, forming a right-angled triangle.

Solution:

a^2 + b^2 = c^2

Explanation:

25\text{ m}