Find Missing Sides of Triangles Using 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

If one leg of a right triangle is 6 units and the other leg is 8 units, what is the length of the hypotenuse?

Back

10 units (Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10).

Front

What is a right triangle?

Back

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

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

If a right triangle has a hypotenuse of 15 units and one leg of 9 units, what is the length of the other leg?

Back

12 units (Using the Pythagorean Theorem: c² = a² + b², 15² = 9² + b², 225 = 81 + b², b² = 144, b = 12).

Front

Which of the following sets of side lengths form a right triangle: 5, 12, 13 or 7, 24, 25?

Back

Both sets form right triangles (5² + 12² = 13² and 7² + 24² = 25²).

Front

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

Back

The formula is: leg = √(hypotenuse² - other leg²).

Front

If a right triangle has legs of 3 units and 4 units, what is the length of the hypotenuse?

Back

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

Front

Which set of side lengths does not form a right triangle: 8, 15, 17 or 9, 12, 15?

Back

9, 12, 15 does not form a right triangle (9² + 12² ≠ 15²).

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.