Pythagorean Theorem

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What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: a² + b² = c².

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What does 'a' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'a' represents the length of one of the two legs (sides) of a right triangle.

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What does 'b' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'b' represents the length of the other leg (side) of a right triangle.

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What does 'c' represent in the Pythagorean Theorem?

Back

In the Pythagorean Theorem, 'c' represents the length of the hypotenuse, which is the side opposite the right angle in a right triangle.

Front

If a = 3 and b = 4, what is c?

Back

Using the Pythagorean Theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5.

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If a = 5 and c = 13, what is b?

Back

Using the Pythagorean Theorem: b² = c² - a² = 13² - 5² = 169 - 25 = 144. Therefore, b = √144 = 12.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the lengths of the two legs (a and b) equals the square of the length of the hypotenuse (c): a² + b² = c².

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²).

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What is the formula to find the length of a leg if the hypotenuse and the other leg are known?

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The formula to find the length of a leg (b) is: b = √(c² - a²).