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5:4 Inequalities for Sides and Angles of a Triangle Objective: Recognize and apply relationships between sides and angles of triangles

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Theorem:If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. A B C 12 9 7 EX. List the angles from greatest to least.

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Theorem: If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. D E F EX: 35° 55° List the sides from shortest to longest.

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EXAMPLE 1.Which is greater, m CBD or m CDB? 2.Is m ADB> m DBA? 3.Which is greater, m CDA or m CBA? D C A B 15 16 10 812

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PRACTICE 1.Name the angle with the least measure in LMN. 2.Which angle in MOT has the greatest measure? 3.Name the greatest of the six angles in the two triangles, LMN and MOT. L N M T O 10 7 6 5 9 8

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EXAMPLE 1. Which side of RTU is the longest? 2. Name the side of UST that is the longest. 3. T RUS 30º 110º

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PRACTICE 1. What is the longest segment in CED? 2. Find the longest segment in ABE. 3. Find the longest segment on the figure. Justify your choice. 4. What is the shortest segment in BCDE? 5. Is the figure drawn to scale? Explain. AE D C B 30º 40º 100º 55º 50º

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Exit Ticket Find the value of x and list the sides of ABC in order for SHORTEST to LONGEST if the angles have the indicated measures. m A = 12x - 9, m B = 62 – 3x, m C = 16x + 2

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