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

Example 1 Use the Exterior Angle Inequality Theorem to list all of the angles whose measures are less than m14. By the Exterior Angle Inequality Theorem, m14 > m2, m14 > m4, m14 > m11, and m14 > m4 + m3, therefore m14 > m3. Answer: The angles that are greater than m14 are 2, 4, 11 and 3.

Example 2: Use the Exterior Angle Inequality Theorem to list all angles whose measures are greater than m5. By the Exterior Angle Inequality Theorem, m10 > m5, m12 > m5, and m17 > m5. Answer: The angles that are greater than m5 are 10, 12 and 17.

Your Turn: 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 m4 b. all angles whose measures are greater than m8 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.

Example 2A: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest. The shortest side is , so the smallest angle is F. The longest side is , so the largest angle is G. The angles from smallest to largest are F, H and G.

Example 2B: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest. mR = 180° – (60° + 72°) = 48° 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

Check It Out! Example 2a Write the angles in order from smallest to largest. The shortest side is , so the smallest angle is B. The longest side is , so the largest angle is C. The angles from smallest to largest are B, A, and C.

Check It Out! Example 2b Write the sides in order from shortest to longest. mE = 180° – (90° + 22°) = 68° 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

Kahoot!

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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