Pythagorean Theorem Test 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.

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees. This can be verified using the Pythagorean Theorem.

Front

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

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If one side of a right triangle is 5 and the other is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169. Therefore, c = √169 = 13.

Front

What is a Pythagorean triple?

Back

A Pythagorean triple consists of three positive integers (a, b, c) that satisfy the Pythagorean Theorem: a² + b² = c². An example is (3, 4, 5).

Front

Can the lengths 15, 12, and 9 form a right triangle?

Back

Yes, because 15² = 12² + 9² (225 = 144 + 81). Thus, they satisfy the Pythagorean Theorem.

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.

Front

How do you determine if a set of three lengths can form a triangle?

Back

To determine if three lengths can form a triangle, they must satisfy the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

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, where the shortest side is opposite the 30-degree angle.