Pythagoram Theorem 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

How do you cancel out the square when solving using Pythagorean Theorem?

Back

Square Root

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, typically referred to as sides a and b.

Front

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

Back

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

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

In a right triangle, if one leg is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

5 (Using the Pythagorean Theorem: c² = a² + b², 13² = 12² + b², 169 = 144 + b², b² = 25, so b = 5).

Front

What is the formula to find the area of a right triangle?

Back

Area = (1/2) * base * height.

Front

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

Back

Yes, it is a right triangle (3² + 4² = 5²).

Front

What is the Pythagorean triplet?

Back

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

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

Use the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the legs.