Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios that make calculations easier. The two main types are 30-60-90 triangles and 45-45-90 triangles.

Front

What is the side length ratio of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2, where 1 is the length of the short leg (opposite the 30° angle), √3 is the length of the longer leg (opposite the 60° angle), and 2 is the length of the hypotenuse.

Front

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

Back

In a 45-45-90 triangle, the hypotenuse is √2 times the length of either leg.

Front

What is the relationship between the angles in a 30-60-90 triangle?

Back

The angles in a 30-60-90 triangle are 30°, 60°, and 90°.

Front

If one leg of a 45-45-90 triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

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

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.

Front

In a 30-60-90 triangle, if the short leg is 4, what is the length of the longer leg?

Back

The longer leg is 4√3.

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180°.

Front

What is the definition of corresponding angles?

Back

Corresponding angles are angles that are in the same position on two parallel lines cut by a transversal.

Front

What is the definition of alternate interior angles?

Back

Alternate interior angles are angles that are on opposite sides of the transversal and inside the two parallel lines.