Triangle Theorems

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, which of the following could be the length of side AC? Options: 16 inches, 5 inches, 32 inches, 29 inches.

Back

16 inches (because 10 + 17 > 16, 10 + 16 > 5, and 17 + 16 > 5).

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

If one angle of a triangle measures 81° and another measures 37°, what is the measure of the third angle?

Back

62° (because 180° - 81° - 37° = 62°).

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 an obtuse triangle?

Back

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

Front

What is a right triangle?

Back

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

Front

What are remote interior angles in relation to an exterior angle?

Back

Remote interior angles are the two angles inside the triangle that are not adjacent to the exterior angle.

Front

If angle W is an exterior angle, which angles are the remote interior angles?

Back

The remote interior angles are the two angles inside the triangle that are not adjacent to angle W.

Front

Can a triangle have two obtuse angles?

Back

No, a triangle cannot have two obtuse angles because the sum of the angles would exceed 180 degrees.