1. 5-3 Inequalities in One Triangle
You found the relationship between the angle measures of a 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.

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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 Draw a scalene triangle. Measure the three sides.
Measure the three angles.
What relationship do you see between the sides and the angles? C B

8. Name the largest and smallest angles9 11 12 A B C

9. Name the largest and smallest anglesF
5.6
5.5
110°

10. List the angles of ΔABC in order from smallest to largest.
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.
Answer: C, A, B

11. Name the longest and shortest segmentsB C
130°
30°
20°

12. Name the longest and shortest segmentsV W X
49°

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

14. 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

15. 5-3 Assignment
Page 348, , 14-19, even