8.7C 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: a² + b² = c².

Front

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

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

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

Back

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

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

In a right triangle, if the lengths of the two legs are 5 units and 12 units, what is the length of the hypotenuse?

Back

c = √(5² + 12²) = √(25 + 144) = √169 = 13 units.

Front

What is the area of a square with a side length of 5 units?

Back

The area of a square is calculated as side². Therefore, area = 5² = 25 square units.

Front

How do you find the length of one leg of a right triangle if you know the hypotenuse and the other leg?

Back

You can use the Pythagorean Theorem: a = √(c² - b²), where c is the hypotenuse and b is the length of the known leg.

Front

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

Back

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

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 shortest side is opposite the 30° angle.

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.