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: c² = a² + b².

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the side opposite the right angle and is always the longest side of the triangle.

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

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5 units.

Front

True or False: The hypotenuse can be shorter than either of the other two sides in a right triangle.

Back

False. The hypotenuse is always the longest side in a right triangle.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

If the hypotenuse is 10 units and one side is 6 units, how do you find the other side?

Back

Use the formula: b² = c² - a². Here, b² = 10² - 6² = 100 - 36 = 64. Therefore, b = √64 = 8 units.

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. The side opposite the 30° angle is the shortest.

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 do you calculate the distance from a point to a line using the Pythagorean Theorem?

Back

Draw a perpendicular line from the point to the line, forming a right triangle. Use the lengths of the sides to apply the Pythagorean Theorem.

Front

If a flagpole is 26 feet high and a string is attached to the top, 18 feet away from the base, how long is the string?

Back

Using the Pythagorean Theorem: c² = 26² + 18² = 676 + 324 = 1000. Therefore, c = √1000 ≈ 31.6 feet.