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 is the formula for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse is a² + b² = c².

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

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

Front

What is the distance between two points (3, 4) and (7, 1) in a coordinate plane?

Back

5 units (using the distance formula: √((x2 - x1)² + (y2 - y1)²) = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5).

Front

What is a right triangle?

Back

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

Front

If a ladder is placed 10 feet away from a wall and reaches a height of 24 feet, how long is the ladder?

Back

26 feet (using the Pythagorean Theorem: 10² + 24² = c²; 100 + 576 = c²; c² = 676; c = 26).

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.

Front

If the lengths of the two legs of a right triangle are equal, what type of triangle is it?

Back

It is an isosceles right triangle.