Pythagorean Theorem & 45-45-90 Triangles

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 a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. The lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

How do you find the length of the hypotenuse in a right triangle?

Back

To find the length of the hypotenuse (c) in a right triangle, use the Pythagorean Theorem: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If one leg of a 45-45-90 triangle is 10, what is the length of the hypotenuse?

Back

The hypotenuse is 10√2, which is approximately 14.14.

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 between two points (x1, y1) and (x2, y2)?

Back

The distance d can be calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the distance between the points (3, 4) and (7, 1)?

Back

The distance is 5 units.

Front

If a rectangular field is 30 yards wide and 40 yards long, what is the diagonal distance across the field?

Back

The diagonal distance is 50 yards, calculated using the Pythagorean Theorem: √(30² + 40²) = 50.

Front

What is the formula for the area of a right triangle?

Back

The area A of a right triangle can be calculated using the formula: A = (1/2) * base * height.

Front

What is the length of the diagonal of a rectangle with sides of length 8 and 6?

Back

The diagonal length is 10 units, calculated using the Pythagorean Theorem: √(8² + 6²) = 10.