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.

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

What is the formula to find the length of a side in a right triangle?

Back

To find the length of a side, you can rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

In a right triangle, if the hypotenuse is 10 units and one side is 6 units, what is the length of the other side?

Back

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

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

How can the Pythagorean Theorem be applied in real life?

Back

The Pythagorean Theorem can be used in various real-life situations, such as determining the distance between two points, calculating heights, and in construction.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²), which calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane.

Front

If a right triangle has a hypotenuse of 13 units and one leg of 5 units, what is the length of the other leg?

Back

12 units (using the Pythagorean Theorem: 13² - 5² = 169 - 25 = 144; √144 = 12).