Pythagorean Theorem Unit Assessment

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

How can you determine if three lengths can form a triangle?

Back

To determine if three lengths can form a triangle, use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are referred to as the legs.

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

What is the simplified form of √196?

Back

The simplified form of √196 is 14.

Front

How do you simplify a radical expression like 5√80?

Back

To simplify 5√80, factor 80 into its prime factors: 80 = 16 * 5. Then, take the square root of 16 (which is 4) out of the radical: 5√80 = 5 * 4√5 = 20√5.

Front

What is an example of a set of lengths that can form a triangle?

Back

An example of a set of lengths that can form a triangle is 9, 9, 9, which satisfies the triangle inequality theorem.

Front

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

Back

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

Front

What is the relationship between the sides of a triangle and the Pythagorean Theorem?

Back

The Pythagorean Theorem applies specifically to right triangles, establishing a relationship between the lengths of the sides: a² + b² = c².

Front

What is the significance of the triangle inequality theorem?

Back

The triangle inequality theorem is significant because it provides a necessary condition for three lengths to form a triangle, ensuring that the sum of any two sides is greater than the third.