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

If a = 3 cm and b = 4 cm, what is the length of the hypotenuse (c)?

Back

Using the Pythagorean Theorem: c² = a² + b² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 cm.

Front

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

Back

False. The Pythagorean Theorem only applies to right triangles.

Front

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

Back

To find the length of a missing side, use the formula: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the other sides.

Front

Find the missing side if a = 6 cm and c = 10 cm.

Back

Using the formula: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √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. The side opposite the 30° angle is half the hypotenuse.

Front

Find the length of the hypotenuse if the two other sides are 8 cm and 15 cm.

Back

Using the Pythagorean Theorem: c = √(8² + 15²) = √(64 + 225) = √289 = 17 cm.

Front

If one side of a right triangle is 12 cm and the hypotenuse is 13 cm, what is the length of the other side?

Back

Using the formula: b = √(c² - a²) = √(13² - 12²) = √(169 - 144) = √25 = 5 cm.

Front

What is the Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². An example is (3, 4, 5).

Front

Find the missing side if a = 9 cm and c = 15 cm.

Back

Using the formula: b = √(c² - a²) = √(15² - 9²) = √(225 - 81) = √144 = 12 cm.