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Class Greeting. Objective: The students will apply Inequalities in One Triangle. Exterior Angle Inequality Theorem. If an is an exterior of a ∆, then its measure is greater than the measure of either of its remote interior s. m 1 > m 3 m 1 > m 4. m 5 > m 3 m 5 > m 2.

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## Class Greeting

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**Objective: The students will apply Inequalities in One**Triangle.**Exterior Angle Inequality Theorem**• If an is an exterior of a ∆, then its measure is greater than the measure of either of its remote interior s. m1 > m 3m 1 > m 4 m5 > m 3m 5 > m 2**Example 1**Use the Exterior Angle Inequality Theorem to list all of the angles whose measures are less than m14. By the Exterior Angle Inequality Theorem, m14 > m2, m14 > m4, m14 > m11, and m14 > m4+m3, therefore m14 > m3. Answer:The angles that are greater than m14 are 2, 4, 11 and 3.**Example 2:**Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than m5. By the Exterior Angle Inequality Theorem, m10 > m5, m12 > m5, andm17 > m5. Answer: The angles that are greater than m5 are 10,12 and17.**Use the Exterior Angle Inequality Theorem to list all of the**angles that satisfy the stated condition. a. all angles whose measures are less than m4 b. all angles whose measures are greater than m8 Your Turn: Answer:5, 2, 8, 7 Answer:4, 9, 5**The positions of the longest and shortest sides of a**triangle are related to the positions of the largest and smallest angles.**The shortest side is , so the smallest angle is F.**The longest side is , so the largest angle is G. Example 2A: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest. The angles from smallest to largest are F, H and G.**The smallest angle is R, so the shortest side is .**The largest angle is Q, so the longest side is . The sides from shortest to longest are Example 2B: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest. mR = 180° – (60° + 72°) = 48°**The shortest side is , so the smallest angle is B.**The longest side is , so the largest angle is C. Check It Out! Example 2a Write the angles in order from smallest to largest. The angles from smallest to largest are B, A, and C.**The smallest angle is D, so the shortest side is .**The largest angle is F, so the longest side is . The sides from shortest to longest are Check It Out! Example 2b Write the sides in order from shortest to longest. mE = 180° – (90° + 22°) = 68°**Lesson Summary:**Objective: The students will apply Inequalities in One Triangle.**Preview of the Next Lesson:**Objective: The students will review for Lesson 5-1 to 5-3 test.

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