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 can be expressed as: c² = a² + b².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

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

Front

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

Back

In a right triangle, the length of the hypotenuse is always greater than either of the other two sides.

Front

How do you classify a triangle with sides 8, 9, and 15?

Back

The triangle is classified as obtuse because 15² > 8² + 9².

Front

What is the formula to find the length of one leg of a right triangle if the hypotenuse and the other leg are known?

Back

If c is the hypotenuse and a is the known leg, the formula is: b = √(c² - a²).

Front

What is the distance from a point to a line in a right triangle context?

Back

The distance from a point to a line can be found using the perpendicular segment from the point to the line.

Front

If a ladder is placed 10 feet away from a house and needs to reach a height of 25 feet, how tall must the ladder be?

Back

Using the Pythagorean Theorem: c² = 10² + 25² = 100 + 625 = 725, so c = √725 ≈ 26.93 feet, which rounds to 27 feet.

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.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem is specifically for right triangles.