Pythagorean Theorem - Georgia Milestone 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 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 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

5 units (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

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

Back

Use the Pythagorean Theorem: check if a² + b² = c², where c is the longest side.

Front

What is the formula to find the length of a diagonal in a rectangle?

Back

The length of the diagonal (d) can be found using the formula: d = √(length² + width²).

Front

In a right triangle with legs of lengths 5 and 12, what is the length of the hypotenuse?

Back

13 units (5² + 12² = 25 + 144 = 169; √169 = 13).

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.

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

If a right triangle has a hypotenuse of 10 and one leg of 6, what is the length of the other leg?

Back

8 units (using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64; √64 = 8).

Front

What is the area of a right triangle with a base of 8 and a height of 6?

Back

24 square units (Area = 1/2 * base * height = 1/2 * 8 * 6).