Understanding Triangle Inequalities and Angle-Side Relationships
Explore the Vocabulary of Exterior Angle Inequality Theorem, Angle-Side Relationship Theorems 5.9 and 5.10. Understand how to order triangel angle measures and side lengths from smallest to largest through examples. Discover the principles governing triangles in terms of angles and side lengths.
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Lesson 5-3 Inequalities in one Triangle
Vocabulary Exterior Angle Inequality Theorem 5.8: The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.
Example 1 A. B. C. D.
Example 1 A. B. C. D.
Vocabulary Angle-Side Relationship #1 Theorem 5.9: If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the side opposite the shorter side.
Vocabulary Angle-Side Relationship #2 Theorem 5.10: If one angle of a triangle has greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Example 2 Order Triangle Angle Measures List the angles of ABC in order from smallest to largest. Answer: C, A, B
Example 2 List the angles of TVX in order from smallest to largest. A. X, T, V X, V, T B. V, T, X C. D. T, V, X
Example 3 Order Triangle Side Lengths List the sides of ABC in order from shortest to longest. The angles from smallest to largest are B, C, and A. The sides opposite these angles are AC, AB, and BC, respectively. So, the sides from shortest to longest are AC, AB, BC. Answer:AC, AB, BC
Example 3 List the sides of RST in order from shortest to longest. A. RS, RT, ST B. RT, RS, ST C. ST, RS, RT D. RS, ST, RT
Example 4 Angle-Side Relationships 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? Answer: So, Ebony should tie the ends marked Y and Z.
Example 4 KITE ASSEMBLY Tanya is following directions for making a kite. She has two congruent triangular pieces of fabric that need to be sewn together along their longest side. The directions say to begin sewing the two pieces of fabric together at their smallest angles. At which two angles should she begin sewing? A. A and D B and F C and E D. A and B B. C.
