Special Triangles

Front

What is a special triangle?

Back

A special triangle is a triangle with specific properties that make calculations easier, such as the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side lengths of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of a leg.

Front

What are the side lengths of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30° angle is x, the length of the side opposite the 60° angle is x√3, and the hypotenuse is 2x.

Front

How do you find the hypotenuse in a 45-45-90 triangle?

Back

To find the hypotenuse, multiply the length of one leg by √2.

Front

How do you find the side lengths in a 30-60-90 triangle?

Back

To find the side lengths, use the ratios: opposite 30° = x, opposite 60° = x√3, hypotenuse = 2x.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

Front

How can you use the Pythagorean theorem with special triangles?

Back

You can use the Pythagorean theorem to verify the side lengths of special triangles or to find missing side lengths.

Front

What is the relationship between the angles and side lengths in special triangles?

Back

In special triangles, specific angle measures correspond to specific ratios of side lengths, making calculations predictable.

Front

What is the significance of simplifying radicals in triangle problems?

Back

Simplifying radicals helps to express side lengths in their simplest form, making them easier to work with and understand.

Front

How do you simplify √8?

Back

√8 can be simplified to 2√2.