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). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 3 feet and the other side is 4 feet, what is the length of the hypotenuse?

Back

5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the square root of 16?

Back

4 (the number that, when multiplied by itself, gives 16).

Front

In a right triangle, if one leg is 5 and the hypotenuse is 13, what is the length of the other leg?

Back

12 (using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If a ladder is 10 feet long and the base is 4 feet from the wall, how high does the ladder reach on the wall?

Back

9 feet (using the Pythagorean Theorem: 4² + h² = 10²; 16 + h² = 100; h² = 84; h = √84 ≈ 9).

Front

What is the opposite operation of squaring a number?

Back

Square root.

Front

If a right triangle has legs of lengths 8 and 15, what is the length of the hypotenuse?

Back

17 (using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289; √289 = 17).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.