Ac1.5bPracticeProblems
- 1. Millau Bridge Sir Norman Foster Point, Lines, Planes, Angles Fallingwaters Frank Lloyd Wright Millenium Park Frank Lloyd Wright 1.5 CE Page 24
- 2. 1.5 CE Page 24 Theorem 1.1 states that two lines intersect in exactly one point. The diagram suggests what would happen if you tried to show that 2 lines were drawn through 2 points. State the postulate that makes this situation impossible. Through any 2 points there is exactly one line. 2. State postulate 6 using the phrase one and only one. Post. 6 Through any two points, there is exactly one line. Through any two points, there is one and only one line.
- 3. 3. Reword the following statement as two statements, one describing existence and one describing uniqueness. Existence: All segments have a midpoint. Uniqueness: A segment has only 1 midpoint. A segment has exactly one midpoint. Postulate 6 is sometimes stated as “Two points determine a line.” 4. Restate Theorem 1-2 using the word determine. Theorem 1-2 If 2 lines intersect, then they intersect in exactly one point. If 2 intersecting lines determine one point.
- 4. Postulate 6 is sometimes stated as “Two points determine a line.” 5. Do 2 intersecting lines determine a plane? 6. Do three points determine a line? Yes. If the points are collinear then they determine 1 line. If the points are non-collinear, then they determine 3 lines. Yes, there are 3 non-collinear points. Also… Theorem 1-3 states that two intersecting lines are in exactly 1 plane.
- 5. 7. Do three points determine a plane? No. If the points are collinear, they don’t. If the points are non-collinear, they do. Sometimes is always answered NO .
- 6. State a postulate, or part of a postulate, that justifies your answer for each exercise. 8. Name 2 points that determine line l. 9. Name three points that determine plane M. 10. Name the intersection of planes M and N. A, C A, B, C also A, B, D also B, C, D
- 7. State a postulate, or part of a postulate, that justifies your answer for each exercise. 11. Does lie in plane M? 12. Does plane N contain any points not on ? Yes, it is just not drawn. Yes, they are just not drawn or labeled. Each plane has an infinite number of points.
- 8. 13. Why does a three-legged support work better than one with four legs? 14. Explain why a four-legged table may rock even if the floor is level. Three legs are always in a plane and therefore are steady and do not rock. Four points may or may not be in a plane. Also most ground is not level. The 4 legs may not be in the same plane. Also over time the four legs move, swell, and are jarred out of position.
- 9. 15. A carpenter checks to see if a board is warped by laying a straightedge across the board in several directions. State the postulate that is related to this procedure. If two points of a line are in the plane, then the line is in the plane. If there is space under the straight edge, then the board is curved or warped.
- 10. 16. Think of the intersection of of the ceiling and the front wall of your classroom. Let the point in the center of the floor be point C. a. Is there a plane that contains line L and point C? b. State the theorem that applies. Through a line and a point not on the line, there is exactly one plane. Yes. Note that this situation has 3 non-collinear points. L L
- 11. C’est fini. Good day and good luck.