Pythagorean Theorem Flashcard

Front

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: a² + b² = c².

Front

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the Pythagorean Theorem holds true: a² + b² = c², where c is the longest side.

Front

What are the side lengths of a right triangle called?

Back

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

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

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

Front

In a right triangle, if one leg is 7 and the hypotenuse is 25, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 25² = 7² + b². Thus, 625 = 49 + b², leading to b² = 576, so b = √576 = 24.

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

The triangle with sides 5, 12, and 13 is a right triangle because it satisfies the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169 = 13².

Front

How do you find the width of a television given its diagonal and height?

Back

Use the Pythagorean Theorem: diagonal² = height² + width². Rearranging gives width = √(diagonal² - height²). For a 17-inch diagonal and 10-inch height, width = √(17² - 10²) = √(289 - 100) = √189 ≈ 13.7 inches.

Front

What is the hypotenuse in a triangle with sides 7, 24, and 25?

Back

The hypotenuse is the longest side, which is 25 in this case.

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean Theorem.

Front

Can a triangle with sides 8, 15, and 17 be a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289 = 17², satisfying the Pythagorean Theorem.