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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the side opposite the right angle in a right triangle and is the longest side.

Front

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

Back

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

Front

Which triangle types can the Pythagorean Theorem be applied to?

Back

The Pythagorean Theorem can only be applied to right triangles.

Front

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

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 5² + 12² = c²; 25 + 144 = c²; 169 = c²; c = 13.

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

What is the term for the two shorter sides of a right triangle?

Back

The two shorter sides are called the legs of the triangle.

Front

If the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8.