Flashcard: Pythagorean Theorem and Special Right 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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If one leg of a right triangle is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

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

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths, such as the 45-45-90 triangle and the 30-60-90 triangle.

Front

In a 45-45-90 triangle, if the legs are of length x, what is the length of the hypotenuse?

Back

The length of the hypotenuse is x√2.

Front

In a 30-60-90 triangle, if the shortest leg is of length x, what are the lengths of the other sides?

Back

The lengths are: the longer leg is x√3 and the hypotenuse is 2x.

Front

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

Back

You can use the Pythagorean Theorem (a² + b² = c²) to find the length of a missing side, where a and b are the legs and c is the hypotenuse.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the ratio of the lengths of the sides is 1 : √3 : 2.

Front

What is the value of y if one leg of a right triangle is 9 and the hypotenuse is 9√2?

Back

Using the Pythagorean Theorem: 9² + y² = (9√2)²; 81 + y² = 162; y² = 81; y = 9.

Front

What is the formula to calculate the area of a right triangle?

Back

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