Inequalities in One Triangle

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

If one angle of a triangle is larger than another, what can be said about the sides opposite those angles?

Back

The side opposite the larger angle is longer than the side opposite the smaller angle.

Front

How do you determine the longest side of a triangle?

Back

To determine the longest side, find the largest angle in the triangle; the side opposite this angle is the longest.

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

If the angles of a triangle are 30°, 60°, and 90°, what is the order of the sides from smallest to largest?

Back

The order of the sides from smallest to largest is: side opposite 30° (shortest), side opposite 60°, side opposite 90° (longest).

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°.

Front

How can you find the measure of an unknown angle in a triangle?

Back

You can find the measure of an unknown angle by subtracting the sum of the known angles from 180°.

Front

What is the definition of an exterior angle of a triangle?

Back

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side.

Front

How is an exterior angle related to the interior angles of a triangle?

Back

An exterior angle is equal to the sum of the two opposite interior angles.

Front

What is the relationship between the sides of a triangle and the angles when two sides are equal?

Back

If two sides of a triangle are equal, the angles opposite those sides are also equal.