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5-3 Inequalities in One Triangle

You found the relationship between the angle measures of a triangle. 5-3 Inequalities in One Triangle. Recognize and apply properties of inequalities to the measures of the angles of a triangle.

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5-3 Inequalities in One Triangle

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  1. You found the relationship between the angle measures of a triangle. 5-3 Inequalities in One Triangle • Recognize and apply properties of inequalities to the measures of the angles of a triangle. • Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.

  2. Page 344

  3. The definition of inequality and the properties of inequalities can be applied to the measures of angles and segments, since these are real numbers. 2 1 3

  4. By the Exterior Angle Inequality Theorem, m14 > m4 and m14 > m11. In addition, m14 > m2 and m14 > m4 + m3, so m14 > m4 and m14 > m3. Since 11 and 9 are vertical angles, they have equal measure, so m14 > m9. m9 > m6 and m9 > m7, so m14 > m6 and m14 > m7.

  5. A. B. C. D.

  6. The Littlest Angle A C • Draw a scalene triangle. • Measure the three sides. • Measure the three angles. • What relationship do you see between the sides and the angles? B

  7. A 9 11 C B 12 Name the largest and smallest angles

  8. D 5.6 110° F E 5.5 Name the largest and smallest angles

  9. The sides from the shortest to longest are AB, BC, and AC. The angles opposite these sides are C,A, and B, respectively. So, according to the Angle-Side Relationship, the angles from smallest to largest are C, A, B. List the angles of ΔABC in order from smallest to largest. Answer:C, A, B

  10. A 30° 130° 20° B C Name the longest and shortest segments

  11. V 49° W X Name the longest and shortest segments

  12. 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 List the sides of ΔABC in order from shortest to longest.

  13. Theorems If two sides of a triangle have unequal lengths, then the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side. If two angles of a triangle have unequal measures, then the side opposite the large angle is longer than the side opposite the smaller angle

  14. 5-3 Assignment • Page 348, 8-12, 14-19, 22-28 even

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