Pythagorean Theorem Word Problems Flashcardizz

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

How do you find the distance between two points using the Pythagorean Theorem?

Back

To find the distance between two points (x1, y1) and (x2, y2) on a coordinate plane, use the formula: distance = √((x2 - x1)² + (y2 - y1)²). This is derived from the Pythagorean Theorem.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse.

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

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

Front

What is the area of a square with a side length of 8 inches?

Back

The area of a square is calculated as side². Therefore, area = 8² = 64 square inches.

Front

How do you calculate the diagonal of a square?

Back

The diagonal (d) of a square can be calculated using the formula: d = side√2.

Front

If a television screen measures 50 inches diagonally and has a width of 30 inches, how do you find the height?

Back

Use the Pythagorean Theorem: height² = diagonal² - width²; height² = 50² - 30²; height² = 2500 - 900; height = √1600 = 40 inches.

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 shortest side is opposite the 30-degree angle.

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.