Week 1 Notes

1. Week 1 Notes • Note, not all slides are here, some you will have to write in other space like paper, but this should help minimize some writing. You figure out your own method.

2. 1.2 – Points, Lines, and Planes (2 days)

3. A definition uses known words to describe a new word. In geometry, points, lines, and planes are undefined terms. Point. Technically, it has no size, but we use a dot that has size to represent it. You use a capital letter to label it. Such as Point A All figures are made of points. This is a LINE. It goes both ways, forever without ending. Once again, it has no thickness, but we use a picture with thickness to describe it. Arrows on both ends say it goes on forever.

4. PLANE, goes on forever, once again has no thickness. Even though it goes on forever, we usually use a parallelogram shape to draw it. To label it, a capital cursive letter can be used, or you can use three points that don’t line up (also known as non-collinear points)

5. Collinear points, points all in one line. Noncollinear points, points NOT all in one line. Coplanar points, points all in one plane. Noncoplanar points, points NOT all in one plane.

6. R I T B F This is a ray This is a line segment, it is a segment, or part of a line T, R are ENDPOINTS ORDER MATTERS

7. l M N O OPPOSITE RAYS – are called opposite rays cuz N is between M and O.

8. Name four coplanar points ABCD or FGHI or some other combination that works l P B Name three collinear points A DAB or AEF or GFJ D C What is the intersection of line l and plane P? E Point A Q G I Which plane has points F,H,I? F J Plane Q H

10. Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common. Draw three noncollinear points A, B, C on plane P. Draw line l not on plane P going through point C.

11. Draw three planes M, N, P meeting at point P. Draw three planes M, N, P meeting on line l. In 3-D, sometimes it helps to imagine a box, or look around the room (but not during a test)

12. 1.3 Segments and Their Measures (1 day)

13. Postulate \ Axiom – A rule that is accepted WITHOUT PROOF. Postulate 1 – Ruler Postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the length of AB. A B

14. AC A B C AB BC SEGMENT ADDITION POSTULATE If B is BETWEEN A and C, then AB + BC = AC. Also If AB + BC = AC, then B is between A and C

15. DS = 30 DU = 5 KS = 7 UC = .5CK D U C K S UK = UC = DC = US = boardwork

16. (x2,y2) (x1,y1)

17. (-5, -2) (4, 1) x1y1x2y2

18. 5 5 H S T R Congruence is shown with marks. The marks say that they are the same size and shape Equals means they have equal length, number value. They are equivalent. Definition of congruent segments: Congruent segments have equal lengths

19. Find the distance between Mr. Kim and each food location. (0, 12) (8, 6) (0, 0) (16, 0) (8, 0)