The 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 can be expressed as: c² = a² + b².

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

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What is the hypotenuse in a right triangle?

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The hypotenuse is the longest side of a right triangle, opposite the right angle. It is denoted as 'c' in the Pythagorean Theorem.

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How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

If one leg of a right triangle is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

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What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula, which calculates the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane, is derived from the Pythagorean Theorem: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

In the context of the Pythagorean Theorem, what does 'solving for y' typically involve?

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'Solving for y' typically involves rearranging the Pythagorean Theorem to isolate y, which may represent one of the legs or the hypotenuse of a right triangle.

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What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides are in a ratio that satisfies the Pythagorean Theorem: 3² + 4² = 5² (9 + 16 = 25). This is a common example of a right triangle.

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How can the Pythagorean Theorem be applied in real-life situations?

Back

The Pythagorean Theorem can be applied in various real-life situations, such as determining the height of a ladder needed to reach a certain height when placed a certain distance away from a wall.

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What is the significance of the Pythagorean Theorem in geometry?

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The Pythagorean Theorem is significant in geometry as it provides a fundamental relationship between the sides of right triangles, which is essential for solving various geometric problems.