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 can be expressed as: c² = a² + b².

Front

What do we call the longest side of a right triangle?

Back

The longest side of a right triangle is called the hypotenuse.

Front

In a right triangle, what are the two shorter sides called?

Back

The two shorter sides of a right triangle are called the legs.

Front

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

Back

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

Front

True or False: The hypotenuse is always opposite the right angle in a right triangle.

Back

True.

Front

If a = 5 and c = 13, what is the length of b?

Back

b = 12 (using the Pythagorean Theorem: 5² + b² = 13², so 25 + b² = 169, thus b² = 144, and b = 12).

Front

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

Back

The relationship is that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a = 6 and b = 8, what is the length of c?

Back

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

Front

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

Back

True.

Front

What is the formula for the Pythagorean Theorem?

Back

The formula is c² = a² + b².