5.6 Inequalities in One Triangle

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

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

Back

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

Front

In triangle ∆ABC, if ∠A > ∠B, what is the relationship between the lengths of sides a and b?

Back

Side a (opposite ∠A) is greater than side b (opposite ∠B), so a > b.

Front

How do you determine the order of sides in a triangle based on the angles?

Back

List the sides in order from smallest to largest based on the angles opposite them: smallest angle corresponds to the shortest side.

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 measures of angles in triangle ∆XYZ are ∠X = 30°, ∠Y = 60°, and ∠Z = 90°, list the sides from smallest to largest.

Back

The sides from smallest to largest are: XY, XZ, YZ.

Front

What is the largest angle in a triangle?

Back

The largest angle in a triangle is the one opposite the longest side.

Front

In triangle ∆DEF, if ∠D = 40° and ∠E = 70°, what can be said about the side lengths?

Back

Side opposite ∠E (DE) is longer than side opposite ∠D (DF), so DE > DF.

Front

How do you find the smallest angle in a triangle?

Back

The smallest angle is opposite the shortest side.

Front

What is the sum of the angles in any triangle?

Back

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