GVMS Retake Pythagorean Theorem

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 distance from the base of the wall to the bottom of a ladder leaning against it if the ladder is 10 feet long and the height it reaches is 9 feet?

Back

4 feet (using the Pythagorean Theorem: 10² = 9² + b²; 100 = 81 + b²; b² = 19; b = √19 ≈ 4.36 feet).

Front

In a right triangle, if one leg is 6 inches and the hypotenuse is 10 inches, what is the length of the other leg?

Back

8 inches (using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8).

Front

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

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

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

Back

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

Front

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

Back

The sum of the squares of the two legs equals the square of the hypotenuse.

Front

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

Back

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

Front

What is a right triangle?

Back

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