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 is expressed as a² + b² = c².

Front

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

Back

The formula to find the hypotenuse (c) in a right triangle is c = √(a² + b²).

Front

In the Pythagorean Theorem, what do 'a' and 'b' represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the two legs (the sides that form the right angle) of a right triangle.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

How can you determine if three sides can form a right triangle?

Back

To determine if three sides can form a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides (a² + b² = c²).

Front

What is the hypotenuse of a right triangle with sides 5 and 12?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

Can the sides 8, 15, and 17 form a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289, and 17² = 289.

Front

What is the relationship between the sides in the Pythagorean Theorem?

Back

The relationship is a² + b² = c², where c is the hypotenuse.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, and 25² = 625.

Front

What is the Pythagorean triple?

Back

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