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 c² = a² + b².

Front

What is the longest side of a right triangle called?

Back

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

Front

What are the two shorter sides of a right triangle called?

Back

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

Front

If one leg of a right triangle is 30 cm and the other leg is 40 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 30² + 40² = 900 + 1600 = 2500, so c = √2500 = 50 cm.

Front

True or False: The Pythagorean Theorem can only be applied to right triangles.

Back

True.

Front

What is the formula for finding the length of a missing side in a right triangle using the Pythagorean Theorem?

Back

The formula is c² = a² + b², where c is the hypotenuse and a and b are the legs.

Front

If the hypotenuse of a right triangle is 13 cm and one leg is 5 cm, how do you find the length of the other leg?

Back

Use the formula: b² = c² - a². Here, b² = 13² - 5² = 169 - 25 = 144, so b = √144 = 12 cm.

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem, it is not a right triangle.

Front

In the equation c² = a² + b², what do a and b represent?

Back

In the equation, a and b represent the lengths of the legs of the right triangle.

Front

Can the Pythagorean Theorem be used in three-dimensional geometry?

Back

No, the Pythagorean Theorem specifically applies to two-dimensional right triangles.