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: c² = a² + b².

Front

What is a 30-60-90 triangle?

Back

A 30-60-90 triangle is a special right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

How do you find the length of the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by 2.

Front

How do you find the length of the long leg in a 30-60-90 triangle if the short leg is known?

Back

Multiply the length of the short leg by √3.

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is a special right triangle where the angles measure 45 degrees, 45 degrees, and 90 degrees. The sides are in the ratio 1:1:√2.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle if one leg is known?

Back

Multiply the length of one leg by √2.

Front

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

Back

Each leg is 10/√2 or 5√2.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

Front

What is the formula to find the area of a triangle?

Back

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

Front

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

Back

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