Warm Up 5.2 Skills Check

Inequalities in One Triangle 5.3 Notes Inequalities in One Triangle

Definition of Inequality

Definition of Inequality The definition of inequality and the properties of inequalities can be applied to the measures of angles and segments, since these are real numbers. Consider Ð1, Ð2, and Ð3 in the figure shown. By the Exterior Angle Theorem, you know that mÐ1 = mÐ2 + mÐ3. Since the angle measures are positive numbers, we can also say that mÐ1 > mÐ2 and mÐ1 > mÐ3 by the definition of inequality.

Exterior Angle Inequality

Example 1 Use the diagram to the right. a) Use the Exterior Angle Inequality Theorem to list all angles whose measures are less than mÐ14.

Example 1 b) Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than mÐ5.

Angle side relationships The longest side and largest angle of ∆ABC are opposite each other. Likewise, the shortest side and smallest angle are opposite each other.

Angle Side Relationships

Example 2 List the angles of ΔABC in order from smallest to largest.

Example 3 List the sides of ΔABC in order from shortest to longest.

Example 4 Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie?