Pythagorean Theorem

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 length of a line segment between two points (x1, y1) and (x2, y2)?

Back

The length of a line segment can be found using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

If one side of a right triangle is 3 and the other side is 4, what is the length of the hypotenuse?

Back

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

Front

What is the hypotenuse of a right triangle with legs measuring 5 and 12?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.

Front

How do you find the missing side of a right triangle if you know the hypotenuse and one leg?

Back

Rearrange the Pythagorean Theorem: a² = c² - b² (if b is the known leg).

Front

What is the length of the diagonal of a rectangle with width 50 yards and length 100 yards?

Back

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

Front

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

Back

Using the Pythagorean Theorem: b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 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 you verify if a triangle is a right triangle using the Pythagorean Theorem?

Back

If the lengths of the sides a, b, and c satisfy the equation a² + b² = c², then the triangle is a right triangle.