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: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is a hypotenuse in a right triangle?

Back

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

Front

If a triangle has sides measuring 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is the simplified form of √(a²)?

Back

The simplified form of √(a²) is |a|, which represents the absolute value of a.

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.

Front

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

Back

The area of a right triangle can be found using the formula: Area = (1/2) * base * height.

Front

How do you simplify the expression 5√80?

Back

5√80 can be simplified to 20√5 by factoring 80 into 16 and 5, since √16 = 4.

Front

What is the value of the hypotenuse if one side is 10 and the other side is 24?

Back

Using the Pythagorean theorem: c = √(10² + 24²) = √(100 + 576) = √676 = 26.

Front

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means to rewrite it in its simplest form, removing any perfect square factors.