Points, Lines and Planes Answers

Geometry/Trig Unit 1 Packet finitions: Term Name: Section 1-2: Points, Lines and Planes Diagram in space Point-represents a single location Line-extends in two directions without ending 1-dimensional Plane-a 2-dimensional figure that extends in both directions A 2-dimensional Notation. CAPITAL LETTER lowercase letter line m OR two letters of points on the line AB capital 3 or 4 CAPITAL letters. of points on the plane P D C one CAPITAL letter Space - set of all points Has three dimensions Relationships between Points, Lines, and Planes Collinear points: points that lie on the same line coplanar points: lie in the same plane non-coplar G A=intersection/interiects Intersection of two figures: set Examples: of points that are in both figures Intersection of two lines = poin A D E H G 0.7 #1-10, 11-20 Intersection of two planes = line line Aplane-point line planen plane A plane = point K 1 Classify each statement as true or false. (Write 7 or F.) 3. overleftrightarrow AB is in plane M. 4. M contains overleftrightarrow CD . F 5. overleftrightarrow AB intersects Nat E. F 6. overleftrightarrow AB intersects overleftrightarrow CD at D. T 7. F is in plane N. F 8. B is in plane N. T 9. A, D, and Fare coplanar. T 10. N contains C, D, E, and F F AM N 11. E is on overleftrightarrow CD . T 12. C, D, and E are collinear. T Exs. 3-12 14. E, H, G F 16. E. B. CH Name each of the following. 17. Three lines that intersect at point E FE AE EH Name a fourth point that is in the same plane as the given points. 13. A, B, FE 15. C, G, EA A E F B D G C Exs. 13-20 18. The plane that does not intersect plane FOHE ABCP 19. Two planes that intersect in CÔ CG BF COHG 20. Three planes that intersect at point D ABCD CGHD AEDH Section 1-5: Postulates and Theorems Relating Points, Lines, and Planes A postulate is a statement/ rule that is accepted without proof Postulate 5: A line contains at least 2 points A plane contains at least 3 points • Space contains at least 4 points not all in one plane Postulate 6: Through any two points there is exactly one line Postulate 7: Through any 3 piane points there is at least one Through any 3 Postulate 8: non-collinear points, there is exactly one plane If two points are in a plane, then the line that contains the points is in that plane. "postulate 9: If 2 planes intersect, then their intersection is aline. 2 A theorem is a statement that has been proven Theorem 1-1 If two lines intersect, then they intersect in exactly o one point Theorem 1-2 Through a line and a point not on that line, there is exactly one. plane Theorem 1-3 If two lines exactly intersect, then exach one plane contains the lines. Always, Sometimes, or Never. 1. Two points A lie exactly in the same line. 2. Three points lie in exactly one line. 3. Three points S lie in exactly one plane. 4. Three collinear points N lie in exactly one plane. 5. Two planes S intersect. 6. Two intersecting planes N exactly one point. intersect in 7. Two intersecting planes. line. A intersect in a B. Two lines A intersect at exactly one point. 9. Two intersecting lines A lie in exactly one plane. 10. Two intersecting lines. exactly one point. A intersect at 11. A line and a point not on that line N more than one plane. lie in 12. A line N contains exactly one point. 13. When A and B are in a plane, AB is that plane. A in Classify each statement as true or false. 1. Two points can lie in each of two different lines. F 2. Three noncollinear points can lie in each of two different planes. 3. Three collinear points lie in only one plane. F 4. Two intersecting lines are contained in exactly one plane. T 5. If two lines intersect, then they intersect in exactly one point. T 6. If two planes intersect, then their intersection is a line. T Name each of the following. 7. The plane that contains BF and FG BFG 8. The plane that contains points B, F, and H BFH 9. The plane that intersects ADHE in AE ABEF .The plane that doesn't intersect ABCD FFGH 11. The intersection of planes ADHE, DCGH, and ABCD). D A D E C H Exs. 7-18 G 12. The plane that doesn't contain overleftrightarrow DG and doesn't intersect overleftrightarrow DC ABEF 13. Two lines that don't intersect plane EFGH AD BC AB DC A 14. Three planes that don't intersect overleftrightarrow CG and don't contain overleftrightarrow CG ABEF AEDH one Write the postulate or theorem that justifies the statement about the diagram. E 15. Plane BCGF is the only plane containing overleftrightarrow FG and point C. Thm1-2 Exs. 7-18 16. Lines overleftrightarrow BF and overleftrightarrow FG intersect in only one point. Tom 1-1 17. overleftrightarrow FH contained in the plane FGHE. postulate & 18. Planes ADHE and EFGH intersect in only one line. postulate 9 Section 1-3: Segments, Rays, and Distance Definitions: Term Diagram Notation Segment-two points on a line and all points between them A B overline AB Ray-an endpoint all collinear a particular direction and points in A B C vec AB Opposite rays-rays that point in opposite directions with a common. endpoint 8 D G A B vec AB and vec AC Length of a segment distance between the endpoints of a segment b = length of segment AB, equals a number or variable Postulate 1: . The points on a line can be paired with the real numbers such that any two points can have coordinates 0 and 1. . Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates. T So basically, the Ruler Postulate allows us to use a unit of measure (inches, centimeters, etc.)