Pythagorean Theorem and Triples

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 is expressed as: a² + b² = c².

Front

What is a Pythagorean Triple?

Back

A Pythagorean Triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (6, 8, 10).

Front

Is the statement 'Side c on a triangle is ALWAYS the shortest' true or false?

Back

False. In a right triangle, side c is the hypotenuse and is the longest side.

Front

Calculate the hypotenuse if one side is 6 and the other side is 8.

Back

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

Front

Identify a Pythagorean Triple from the following: 4, 4, 8; 6, 8, 10; 1, 2, 3; 10, 15, 25.

Back

6, 8, 10 is a Pythagorean Triple.

Front

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

Back

The formula is c = √(a² + b²).

Front

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

Back

Using the Pythagorean Theorem: c² = 9² + 12² = 81 + 144 = 225, so c = √225 = 15.

Front

What are the first three Pythagorean Triples?

Back

The first three Pythagorean Triples are (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Front

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

Back

Using the Pythagorean Theorem: b² = 13² - 5² = 169 - 25 = 144, so b = √144 = 12.

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.