Pythagorean Theorem Review

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

In a right triangle, which side is the longest?

Back

The hypotenuse (side c) is always the longest side in a right triangle.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

Front

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

Back

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

Front

If the hypotenuse of a right triangle is 13 and one side is 5, what is the length of the other side?

Back

Using the Pythagorean Theorem: 13² = 5² + b²; 169 = 25 + b²; b² = 144; b = 12.

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

Can the Pythagorean Theorem be used for obtuse or acute triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the length of the diagonal of a rectangle with sides 6 in and 8 in?

Back

Using the Pythagorean Theorem: d² = 6² + 8²; d² = 36 + 64; d = 10 in.

Front

If a right triangle has sides of length 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 12²; c² = 81 + 144; c = 15.