3 + 2 + 1 = 6 5 + 4 + 3 + 2 + 1 = 15 7 + 6 + ……+

Name - _______________________Per______Assignment 2.5 – Postulates and Paragraph ProofsDetermine the number of line segments that can be drawn connecting eachpair of points.1. 2. 3.3 + 2 + 1 = 6 5 + 4 + 3 + 2 + 1 = 15 7 + 6 + ……+ 1 = 28Determine whether the following statements are always, sometimes, ornever true. Explain.4. Three collinear points determine a plane.5. Two points A and B determine a line.6. A plane contains at least three lines.7. The intersection of two planes contains at least two points.8. If three planes have a point in common, then they have a whole line incommon.Assignment 2.5 - Page 1

In the figure, DG and DP line in plane J and H lines on DG .State the postulate that can be used to show each statementis true.9. G and P are collinear.10. Points D, H, and P are coplanar.11. PROOF: In the figure at the right, point B is the midpoint of AC and Cis the midpoint of BD . Write a paragraph proofto prove that AB = CD.12. In the figure, E is the midpoint of AB and CD ,and AB = CD. Write a paragraph proof toprove that AE ED .Assignment 2.5 - Page 2

13. AIRLINES: An airline company wants to provide service to SanFrancisco, Los Angeles, Chicago, Dallas, Washington D.C., and NewYork City. The company CEO draws lines between each pair of citiesin the list on a map. No three of the cities are collinear. How manylines did the CEO draw?5 + 4 + 3 + 2 + 1 = 15FRIENDSHIPS: For Exercises 14 and 15, use the following information.A small company has 16 employees. The owner of the company becameconcerned that the employees did not know each other very well. Hedecided to make a picture of the friendships in the company. He placed 16points on a sheet of paper in such a way that no 3 were collinear. Eachpoint represented a different employee. He then asked each employeewho their friends were and connected two points with a line segment if theyrepresented friends.14. What is the maximum number of line segments that can be drawnbetween pairs among the 16 points?15 + 14 + 13 + ………..+ 1 = 12015. When the owner finished the picture, he found that his company wassplit into two groups, one with 10 people and the other with 6. Thepeople within a group were all friends, but nobody from one group wasa friend of anybody from the other group. How many line segmentswere there?9 + 8 + … + 1 = 55 5 + 4 + 3 + 2 + 1 = 1545 + 15 = 60Assignment 2.5 - Page 3