8th Grade Vocab: Pythagorean Theorem

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What is the Pythagorean Theorem?

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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: a² + b² = c².

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What is a right triangle?

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A right triangle is a triangle that has one angle measuring 90 degrees.

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What are the sides of a right triangle called?

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The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

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How do you find the length of the hypotenuse using the Pythagorean Theorem?

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To find the length of the hypotenuse, use the formula c = √(a² + b²), where a and b are the lengths of the legs.

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

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In a 3-4-5 triangle, the lengths of the sides are in the ratio 3:4:5, which satisfies the Pythagorean Theorem (3² + 4² = 5²).

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What is an example of using the Pythagorean Theorem in real life?

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An example is determining the height of a ladder leaning against a wall. If the base of the ladder is 3 feet from the wall and the ladder is 5 feet long, you can find the height using the Pythagorean Theorem.

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What is the converse of the Pythagorean Theorem?

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The converse of the Pythagorean Theorem states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

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What is a perfect square?

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A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

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What is the distance formula derived from the Pythagorean Theorem?

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

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What is the significance of the Pythagorean Theorem in geometry?

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The Pythagorean Theorem is fundamental in geometry as it helps in calculating distances, constructing right angles, and solving various geometric problems.