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

What is the formula to find the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).

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, so c = √25 = 5 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 shortest side is opposite the 30° 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.

Front

How do you find the length of the diagonal of a rectangle?

Back

Use the Pythagorean Theorem: If the rectangle has width (w) and length (l), the diagonal (d) can be found using d = √(w² + l²).

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

Using the distance formula: d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5 units.

Front

If a rectangular field is 50 yards wide and 100 yards long, how far is the diagonal?

Back

Using the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √12500 = 111.8 yards.

Front

What is the hypotenuse of a right triangle with legs measuring 6 units and 8 units?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 units.

Front

What is the area of a right triangle with a base of 5 units and a height of 12 units?

Back

Area = (1/2) * base * height = (1/2) * 5 * 12 = 30 square units.