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). Formula: a² + b² = c².

Front

What is the formula to find a missing leg of a right triangle?

Back

To find a missing leg (a) of a right triangle, use the formula: c² - b² = a².

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 cm.

Front

What is the length of the missing side if one leg is 5 cm and the hypotenuse is 13 cm?

Back

Using the formula: a² = c² - b², we have a² = 13² - 5² = 169 - 25 = 144. Therefore, a = √144 = 12 cm.

Front

What does 'hypotenuse' mean?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

Back

Using the formula: b² = c² - a², we have b² = 10² - 6² = 100 - 36 = 64. Therefore, b = √64 = 8 cm.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How can you check if a triangle is a right triangle using the Pythagorean Theorem?

Back

To check if a triangle is a right triangle, verify if a² + b² = c² holds true for the lengths of the sides.