Pythagorean Theorem Review

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.

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What are the legs of a right triangle?

Back

The legs of a right triangle are the two shorter sides that form the right angle.

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem formula (a² + b² = c²) to solve for the unknown side. For example, if you know the lengths of the hypotenuse and one leg, you can find the other leg by using: a = √(c² - b²).

Front

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

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height, where the base and height are the lengths of the two legs.

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 relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30-degree angle is half the length of the hypotenuse, and the length of the side opposite the 60-degree angle is √3 times the length of the shorter leg.

Front

How can you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then pair the factors. Each pair can be taken out of the radical as a single factor.

Front

What is the significance of the radical in the context of the Pythagorean Theorem?

Back

The radical is often used to express the length of a side when the Pythagorean Theorem results in a non-perfect square. It represents the exact length of the side.

Front

What is a right triangle?

Back

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