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Pythagorean Theorem Explained

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Questions and Answers

What does the Pythagorean Theorem state about the relationship between the sides of a right triangle?

The hypotenuse is always half the length of the longest side.

The square of the hypotenuse is equal to the sum of the squares of the other two sides. (correct)

The sum of the two shorter sides is equal to the hypotenuse.

The length of each side must be the same.

In the example provided, what are the lengths of sides AB and BC used in the calculation?

9 cm and 12 cm

8 cm and 5 cm (correct)

10 cm and 3 cm

6 cm and 4 cm

How do you find the length of the diagonal AC using the Pythagorean Theorem?

By taking the square root of the sum of the squares of AB and BC (correct)

By adding the lengths of sides AB and BC

By subtracting the shorter side from the longer side

By multiplying the lengths of sides AB and BC

What is the calculated value of AC² in the example provided?

<p>89</p> Signup and view all the answers

What is the approximate length of diagonal AC after performing the calculations?

<p>9.4 cm</p> Signup and view all the answers

Study Notes

Pythagorean Theorem Explained

The example uses a rectangle ABC with sides AB = 8 cm and BC = 5 cm.
We are asked to find the length of the diagonal AC, which is also the hypotenuse of the right triangle ABC.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
The formula is: hypotenuse² = side1² + side2²
The sides AB and BC are known, so we can plug them into the formula: AC² = AB² + BC²
The values are substituted: AC² = 8² + 5²
The calculations are made: AC² = 64 + 25 = 89
To find the length of AC, we take the square root of both sides: AC = √89
The final answer is that AC is approximately 9.4 cm.

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Description

This quiz explains the Pythagorean Theorem using a rectangle example with sides measuring 8 cm and 5 cm. It details how to calculate the length of the diagonal by applying the theorem, illustrating the process with clear steps and calculations. Perfect for students learning about right triangles and geometry!