Pythagorean Theorem & Converse Flashcard

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

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

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 of the triangle.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, it is a right triangle because 3² + 4² = 5² (9 + 16 = 25).

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

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

What is the formula to calculate the hypotenuse?

Back

The formula to calculate the hypotenuse (c) is: c = √(a² + b²).

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if in a triangle, the square of one side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Front

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes, it is a right triangle because 8² + 15² = 17² (64 + 225 = 289).

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is significant because it is always the longest side and is used to determine if a triangle is a right triangle using the Pythagorean Theorem.