Pythagorean Thereom

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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

If one side of a right triangle is 3 and the other side 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

What is the formula to find the length of the 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 the hypotenuse of a right triangle is 10 and one side is 6, what is the length of the other side?

Back

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

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

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

Back

No, the Pythagorean Theorem is specifically for right triangles.

Front

What is the value of x if a right triangle has sides of length 8 and 15?

Back

Using the Pythagorean Theorem: 8² + 15² = x²; 64 + 225 = x²; 289 = x²; x = 17.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (3, 4, 5).

Front

If a right triangle has one side of length 12 and the hypotenuse of length 13, what is the length of the other side?

Back

Using the Pythagorean Theorem: 12² + b² = 13²; 144 + b² = 169; b² = 25; b = 5.