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5.3 Notes : Inequalities in One Triangle

Vocabulary   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 measure of angle 14.

Example 1: b) Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than measure angle 5.

Vocabulary: Longest Side Vs. Longest Angle   Longest Side Vs. Longest Angle Smallest Side Vs. Shortest Side Angle-Side Relationships in Triangles (5.9) Angle- Side Relationships in Triangles (5.10)

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

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

Example 4: Example 4: HAIR ACCESSORIES 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?

Example 5: List the angles of each triangle in order from smallest to largest.

Example 6: List the angles of each triangle in order from smallest to largest.

Example 7: List the angles of each triangle in order from smallest to largest. ∆XYZ, where XY = 25, YZ = 11, and XZ = 15

Example 8: List the sides of each triangle in order from shortest to longest.

Example 9: List the sides of each triangle in order from shortest to longest.

5.1-5.3 Vocabulary Skills Check Match each word to the sentence in which it best fills in the blank. Write your answer on the line to the left. _____1) The point of intersection of the angle bisectors in a triangle is called the_?_.   _____2) The _?_ divides the medians in a triangle into the parts. _____3) The centroid is the intersection of the_?_in a triangle. _____4) The circumcenter is equidistant from the _?_in a triangle. _____5) The incenter is equidistant from the_?_in a triangle _____6) The point of intersection of the perpendicular bisectors in a triangle is called the_?_. _____7) The altitudes in a triangle intersect at a point called the _?_.

Summary! List the sides from biggest to smallest. Write your answer as an inequality.

Summary! b) List the angles from largest to smallest. Write your answer as an inequality. W P A 25 15 12