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 longest side of a right triangle called?

Back

Hypotenuse.

Front

How do you find the length of the hypotenuse using the Pythagorean Theorem?

Back

To find the hypotenuse, use the formula: c = √(a² + b²).

Front

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

Back

To find a missing leg (a or b), rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

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

Back

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

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

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

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.

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.

Front

What is the formula to calculate the area of a right triangle?

Back

Area = (1/2) * base * height.

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to determine distances and angles.