Pythagorean Theorem Challenge

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as: a² + b² = c².

Front

In a right triangle, what do we call the longest side?

Back

The longest side of a right triangle is called the hypotenuse.

Front

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

Back

5 units (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, and √25 = 5).

Front

What is a right triangle?

Back

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

Front

If the hypotenuse of a right triangle is 13 units and one leg is 5 units, how do you find the other leg?

Back

Use the Pythagorean Theorem: a² + 5² = 13². Solve for a: a² + 25 = 169, so a² = 144, and a = 12 units.

Front

What is the formula to find the length of the diagonal of a rectangle?

Back

The formula is: diagonal = √(length² + width²).

Front

If a ladder is 10 feet long and the base is 6 feet away from the wall, how high does the ladder reach?

Back

Using the Pythagorean Theorem: height = √(10² - 6²) = √(100 - 36) = √64 = 8 feet.

Front

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

Back

The relationship is defined by the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

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

Back

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

Front

What do we call the two shorter sides of a right triangle?

Back

The two shorter sides are called the legs.