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 a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (a and b) and the hypotenuse (c). The hypotenuse is the longest side, opposite the right angle.

Front

If a = 3 and b = 4, what is c?

Back

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

Front

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

Back

To find the length of a missing side, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

What is the formula to find the hypotenuse?

Back

The formula to find the hypotenuse (c) is c = √(a² + b²).

Front

What is the formula to find a leg of a right triangle?

Back

The formula to find a leg (a or b) is a = √(c² - b²) or b = √(c² - a²).

Front

If c = 10 and a = 6, what is b?

Back

b = 8 (using the Pythagorean Theorem: 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √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. The shortest side is opposite the 30-degree 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.