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). It is expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

To find the length of the hypotenuse: c = √(a² + b²). To find the length of a leg: a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

In a right triangle, the hypotenuse is always the longest side, and it is opposite the right angle.

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

Using the Pythagorean Theorem: c² = 10² + 24²; c² = 100 + 576; c = √676; c = 26 feet.

Front

What is the converse of the Pythagorean Theorem?

Back

If a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

What are the side lengths of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

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).