Pythagorean Theorem

Discover the relationship between the sides of a right triangle and learn to calculate distances.

8th Grade

Geometry

~45 min

🎮 Interactive Activity: Pythagorean Calculator

Calculate the hypotenuse using the Pythagorean theorem!

a² + b² = c²

a = 3, b = 4

🎮 Interactive Activity: Right Triangle Explorer

Explore right triangles and their properties!

Leg 1: 5, Leg 2: 12

1. What is the Pythagorean Theorem?

📚 Theorem Definition

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the two legs.

a² + b² = c²

• a and b are the legs (shorter sides)

• c is the hypotenuse (longest side, opposite the right angle)

• Only applies to right triangles (90° angle)

Right Triangle

Has one 90° angle
Two legs and one hypotenuse

Hypotenuse

Longest side
Opposite the right angle

2. Using the Formula

3. Converse of the Pythagorean Theorem

4. Distance Formula

5. Real-World Applications

6. Worked Examples

7. Frequently Asked Questions

Practice Time!

Practice Quiz

Questions

Correct

Score

In a right triangle with legs 3 and 4, what is the hypotenuse?

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What is the Pythagorean theorem formula?

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If the hypotenuse is 13 and one leg is 5, what is the other leg?

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Which triangle can use the Pythagorean theorem?

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If a = 6 and b = 8, what is c?

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What is the longest side of a right triangle called?

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If c = 15 and a = 9, what is b?

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A triangle has sides 5, 12, and 13. Is it a right triangle?

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What is the distance formula derived from?

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If a right triangle has legs of 7 and 24, what is the hypotenuse?

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