Pythagorean Theorem STAAR Review

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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.

Front

What is the formula to find the length of the hypotenuse in a right triangle?

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The formula to find the length of the hypotenuse (c) in a right triangle is c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

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

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To find the length of a missing side in a right triangle, use the Pythagorean Theorem. If you know the lengths of two sides, you can rearrange the formula a² + b² = c² to solve for the missing side.

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What is the area of a square?

Back

The area of a square is calculated by squaring the length of one of its sides. The formula is: Area = side².

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If the area of a square is 25 in², what is the length of one side?

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To find the length of one side of a square with an area of 25 in², take the square root of the area: side = √25 = 5 in.

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What is the relationship between the areas of squares constructed on the sides of a right triangle?

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The areas of the squares constructed on the two shorter sides of a right triangle add up to the area of the square constructed on the hypotenuse. This is a direct consequence of the Pythagorean Theorem.

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How do you calculate the diagonal length of a rectangle?

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The diagonal length (d) of a rectangle can be calculated using the Pythagorean Theorem: d = √(length² + width²).

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What is the length of the diagonal of a piece of paper that is 11 inches tall and 8.5 inches wide?

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Using the formula for the diagonal of a rectangle: d = √(11² + 8.5²) = √(121 + 72.25) = √193.25 ≈ 13.9 in.

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What is the significance of the Pythagorean Theorem in real-world applications?

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The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to determine distances and relationships between different points.

Front

What is a right triangle?

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A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.