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, such as 30-60-90 and 45-45-90 triangles.

Front

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

Back

In a 30-60-90 triangle, the side lengths are in the ratio 1 : √3 : 2.

Front

What are the side length ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the side lengths are in the ratio 1 : 1 : √2.

Front

How can you determine if three lengths can form a triangle?

Back

Use the triangle inequality theorem: the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Can a triangle have side lengths of 4, 7, and 18?

Back

No, because 4 + 7 is not greater than 18.

Front

What type of triangle is formed by sides of lengths 4, 6, and 7?

Back

An acute triangle, because all angles are less than 90 degrees.

Front

What is the definition of an acute triangle?

Back

An acute triangle is a triangle where all three interior angles are less than 90 degrees.

Front

What is the definition of an obtuse triangle?

Back

An obtuse triangle is a triangle that has one interior angle greater than 90 degrees.

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one interior angle equal to 90 degrees.