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 the 45°-45°-90° triangle and the 30°-60°-90° triangle.

Front

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

Back

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

Front

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

Back

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

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

Back

Acute triangle.

Front

Can a triangle have sides of lengths 3, 8, and 9?

Back

Yes, these lengths can form a triangle.

Front

What type of triangle is formed by sides of lengths 10, 18, and 40?

Back

Not a triangle.

Front

What is an obtuse triangle?

Back

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

Front

What is an acute triangle?

Back

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

Front

What is a right triangle?

Back

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