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 the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If a triangle has sides a=3 and b=4, what is the length of side c?

Back

c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides. If a² + b² = c², then it is a right triangle.

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

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

Back

Using the Pythagorean Theorem: b = √(c² - a²) = √(10² - 6²) = √(100 - 36) = √64 = 8 cm.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x₁, y₁) and (x₂, y₂) is: d = √((x₂ - x₁)² + (y₂ - y₁)²).

Front

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

Back

Using the Pythagorean Theorem: d = √(6² + 8²) = √(36 + 64) = √100 = 10 m.