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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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C 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. EX. 7 12 A B 9 List the angles from greatest to least.

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EX: D 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. 35° 55° E F List the sides from shortest to longest.

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**EXAMPLE Which is greater, mCBD or mCDB? C Is mADB> mDBA? D**

Which is greater, mCDA or mCBA? C 15 D 8 12 16 A 10 B

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**PRACTICE Name the angle with the least measure in ▲LMN.**

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

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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 30º 110º R U S

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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. A E 55º D 50º 30º 40º 100º C B

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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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The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

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