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11-1B Inequalities in a Triangle What is orienteering? What is the relationship between an angle the opposite side in a triangle? Orienteering • Orienteers can look at a map and visualize their approach to every checkpoint. Such maps are accurate and detailed, and are prepared on a human scale - terrain and features are mapped so that what appears on the map are the features that a human, moving through the area, sees readily. Orienteering skills applied to Geometry Like orienteering, if you look at an accurate figure in Geometry, you may be able to make a good guess at which sides and angles are the largest or smallest. In Geometry, we must be able to prove why. The Littlest Angle 1. 2. 3. 4. A 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 Name the largest and smallest angles A 9 C B 12 Name the largest and smallest angles D 5.6 110° E 5.5 F Name the largest and smallest angles S 4 R 5 5 3.9 Q 5 P Name the longest and shortest segments A 30° 130° B 20° C Name the longest and shortest segments T 65° 60° 75° 45° 50° Q 65° R S Name the longest and shortest segments V 49° W X 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 • What is orienteering? Orienteering uses a detailed map to visualize their approach to every checkpoint. • What is the relationship between an angle the opposite side in a triangle? The largest angle is opposite the longest side and the smallest angle is opposite the shortest side. Assignment 11-1B • Page 717, 1-12, 27-38