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 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

If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?

Back

5 units (Using the Pythagorean Theorem: c² = 3² + 4² => c² = 9 + 16 => c² = 25 => c = 5).

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

If the hypotenuse of a right triangle is 10 units and one leg is 6 units, what is the length of the other leg?

Back

8 units (Using the Pythagorean Theorem: c² = a² + b² => 10² = 6² + b² => 100 = 36 + b² => b² = 64 => b = 8).

Front

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

Back

True.

Front

What is the formula to find the length of the hypotenuse?

Back

c = √(a² + b²).

Front

What is the formula to find the length of a leg if the hypotenuse and one leg are known?

Back

a = √(c² - b²) or b = √(c² - a²).

Front

In a right triangle, if both legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Front

If a right triangle has legs of length 5 units each, what is the length of the hypotenuse?

Back

√(5² + 5²) = √(25 + 25) = √50 = 5√2 units.