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NAME ______________________________________________ DATE 5-2 ____________ PERIOD _____ Skills Practice Inequalities and Triangles Determine which angle has the greatest measure. 3 1. ⬔1, ⬔3, ⬔4 2. ⬔4, ⬔5, ⬔7 3. ⬔2, ⬔3, ⬔6 4. ⬔5, ⬔6, ⬔8 1 2 5 4 6 7 Use the Exterior Angle Inequality Theorem to list all angles that satisfy the stated condition. 8 2 4 7 5. all angles whose measures are less than m⬔1 1 3 5 6 8 9 Lesson 5-2 6. all angles whose measures are less than m⬔9 7. all angles whose measures are greater than m⬔5 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 8. all angles whose measures are greater than m⬔8 Determine the relationship between the measures of the given angles. 9. m⬔ABD, m⬔BAD 23 A 10. m⬔ADB, m⬔BAD B 34 35 C 41 39 D 11. m⬔BCD, m⬔CDB 12. m⬔CBD, m⬔CDB Determine the relationship between the lengths of the given sides. 13. L 苶M 苶, L 苶P 苶 M 83⬚ 57⬚ L 14. 苶 MP 苶, M 苶N 苶 38⬚ 59⬚ 79⬚ N 44⬚ P 15. 苶 MN 苶, N 苶P 苶 Chapter 5 16. 苶 MP 苶, L 苶P 苶 15 Glencoe Geometry NAME ______________________________________________ DATE 5-2 ____________ PERIOD _____ Word Problem Practice Inequalities and Triangles 1. DISTANCE Carl and Rose live on the same straight road. From their balconies they can see a flagpole in the distance. The angle that each person’s line of sight to the flagpole makes with the road is the same. How do their distances from the flagpole compare? 4. SQUARES Matthew has three different squares. He arranges the squares to form a triangle as shown. Based on the information, list the squares in order from the one with the smallest perimeter to the one with the largest perimeter. 2. OBTUSE TRIANGLES Don notices that the side opposite the right angle in a right triangle is always the longest of the three sides. Is this also true of the side opposite the obtuse angle in an obtuse triangle? Explain. 1 2 47˚ 54˚ Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 3. STRING Jake built a triangular structure with three black sticks. He tied one end of a string to vertex M and the other end to a point on the stick opposite M, pulling the string taut. Prove that the length of the string cannot exceed the longer of the two sides of the structure. CITIES For Exercises 5 and Dallas 6, use the following 64˚ information. 59˚ Stella is going to Abilene Texas to visit a friend. As she was looking at a Austin map to see where she might want to go, she noticed the cities Austin, Dallas, and Abilene formed a triangle. She wanted to determine how the distances between the cities were related, so she used a protractor to measure two angles. M string 5. Based on the information in the figure, which of the two cities are nearest to each other? 6. Based on the information in the figure, which of the two cities are farthest apart from each other? Chapter 5 17 Glencoe Geometry Lesson 5-2 3