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 a² + b² = c².

Front

What is the longest side of a right triangle called?

Back

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

Front

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

Back

Using the Pythagorean Theorem: a² + b² = c²; 3² + 4² = c²; 9 + 16 = c²; c² = 25; c = 5.

Front

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

Back

In the equation a² + b² = c², a and b represent the lengths of the two legs (the shorter sides) of a right triangle.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Front

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

Back

You can find the length of one side using the Pythagorean Theorem: rearrange the formula a² + b² = c² to solve for the unknown side.

Front

What is the value of a if b = 35 and c = 37 in the equation a² + b² = c²?

Back

Using the Pythagorean Theorem: a² + 35² = 37²; a² + 1225 = 1369; a² = 144; a = 12.

Front

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 5² + 12² = c²; 25 + 144 = c²; c² = 169; c = 13.

Front

What is the formula to calculate the diagonal of a rectangle?

Back

The formula to calculate the diagonal (d) of a rectangle is d = √(length² + width²).

Front

In a right triangle, which side is always opposite the right angle?

Back

The hypotenuse is always opposite the right angle in a right triangle.