1. Section 1.2 Points, Lines, & Planes 1/17

2. What is a Point? 2/17

3. What is a Line? 3/17

4. What is a Plane? 4/17

5. Representations of Points point A point is the most basic building block of geometry. A point indicates a location. A dot represents or models a point. A point is named with a capital letter. A B 5/17

6. Representations of Lines A line is a one dimensional object that extends indefinitely in two directions A line may be named with two identified points on the line. A line symbol (double-headed arrows) is placed over the letters naming the points on the line. Alternatively, line may be named with a single, lower case letter. QS Read it as: “Line QS” or “Line SQ” Write it as: QS or SQ 6/17

7. Representations of Planes plane A plane has length and width but no thickness. In the figure at the right, the flat surface represents a portion of plane Q. plane A plane may also be named using three points that lie in the plane, such as G, F and E; please note that the three points are not on the same line (Plane GFE). 7/17

8. Representations of Rays ray is a A ray is a part of a line that starts at a point and extends infinitely in one direction. endpoint The point is called the endpoint of the ray. A ray is named its endpoint first. A single arrow (toward the infinite direction) is drawn over the two capitalized letters. CD Read it as: “Ray CD” (the order does matter) Write it as: CD 8/17

9. Representations of Rays Opposite Rays All Opposite Rays Share exactly one point Form a line In Opposite Directions C, D & F are collinear and D is between C & F. CD F DC DF Yes DC CD No 9/17

10. Representations of Segments segment A segment is a part of a line that begins at one point and ends at another. endpoints The points are called the endpoints of the segment. A segment is named by its endpoints. A bar (no arrows) is drawn over the two capitalized letters. RB Read it as: “Segment RB” or “Segment BR” Write it as: RB or BR 10/17

11. Interactions between Points, Lines, & Planes Collinear points Collinear points are points that lie on the same line. In the figure at the right, C, D and F are collinear. C, D and E are non-collinear (not collinear). Any two points are collinear Any two points are collinear. CD E F 11/17

12. Interactions between Points, Lines, & Planes Coplanar points Coplanar points are points that lie in the same plane. In the figure at the right, E, F, G, and H are coplanar. E, F, G, and J are non-coplanar (not coplanar). Any three points are coplanar. Any three points are coplanar. 12/17

13. Interactions between Points, Lines, & Planes The intersection of two lines is a ___________. 13/17

14. Interactions between Points, Lines, & Planes The intersection of two planes is a ___________. 14/17

15. Interactions between Points, Lines, & Planes Through any three non-collinear points there is exactly one _______________. 15/17

16. A Few Questions G D E F H M 16/17

17. HOMEWORK 1.2 P.13 1 – 8, 28, 29, 34, 35, 36, 48, 73 – 75 17/17