Pythagorean Theorem

Front

What does the Pythagorean Theorem state?

Back

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). Formula: a² + b² = c².

Front

What are the legs of a right triangle?

Back

The two sides that form the right angle are called the legs (a and b).

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is denoted as side c.

Front

If a = 3 and b = 4, what is c?

Back

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

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Front

If c = 10 and a = 6, what is b?

Back

b = 8 (using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, b² = 64, b = 8).

Front

What is the formula for finding the length of a side in a right triangle?

Back

The formula is a² + b² = c².

Front

If a = 5 and b = 12, what is c?

Back

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

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The sum of the squares of the two legs equals the square of the hypotenuse.

Front

If c = 50 and b = 30, what is a?

Back

a = 40 (using the Pythagorean Theorem: a² + 30² = 50², so a² + 900 = 2500, a² = 1600, a = 40).