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

What is the formula to find the length of the hypotenuse?

Back

To find the length of the hypotenuse (c) in a right triangle, use the formula: c = √(a² + b²).

Front

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

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.

Front

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

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is always the longest side.

Front

How do you find the length of one side if the hypotenuse and one side are known?

Back

To find the length of one side (a) when the hypotenuse (c) and the other side (b) are known, use the formula: a = √(c² - b²).

Front

What is the value of a if c = 10 cm and b = 6 cm?

Back

Using the formula: a = √(c² - b²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is the value of b if c = 13 cm and a = 5 cm?

Back

Using the formula: b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.

Front

In a right triangle, if one angle is 90 degrees, what can be said about the other two angles?

Back

The other two angles in a right triangle must add up to 90 degrees, making them complementary.

Front

What is the significance of the Pythagorean Theorem in real life?

Back

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and angles.

Front

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

Back

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