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 formula for finding the hypotenuse of a right triangle?

Back

The formula for finding the hypotenuse (c) of a right triangle is: c = √(a² + b²).

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 5 cm and the other side is 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Front

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

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem: a² + b² = c².

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem. Rearrange the formula based on which side is missing: if c is missing, use c = √(a² + b²); if a or b is missing, use a = √(c² - b²) or b = √(c² - a²).

Front

What is the value of the hypotenuse if both legs of a right triangle are equal to 7 cm?

Back

If both legs are equal to 7 cm, then the hypotenuse is c = √(7² + 7²) = √(49 + 49) = √98 ≈ 9.90 cm.

Front

What is the significance of the Pythagorean Theorem in real-world applications?

Back

The Pythagorean Theorem is used in various real-world applications, including construction, navigation, and physics, to determine distances and relationships between different points.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles. For non-right triangles, other methods such as the Law of Cosines are used.

Front

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

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.