Chapter 1 Understanding Points, Lines and Planes 1.1 Point: is a location. A point has no size. P A point denoted by a capital letter. A geometric figure is composed of a set of points. Line: a series of points that extend in two opposite directions without end. There are two ways to name a line. By a small letter By naming two points on the line AB BA B Collinear Points: Points that lie on the same line. A m

Chapter 1 Understanding Points, Lines and Planes 1.1 In the figure below, name three points that are collinear and three points that are not collinear. A B C D E F m k Using the figure to the right, How many other ways can you reference line m? How many ways can you reference line CE? Name a set of collinear points. Name noncollinear points

Chapter 1 Understanding Points, Lines and Planes 1.1 Plane: a flat surface that has no thickness. It contains many lines and extends without end in the directions of all its lines. Name the plane shown in two different ways. Three noncollinear points. Example…plane RST. W Capital letter in cursive (script). Example…plane W Coplanar: points and lines that are in the same plane.

Chapter 1 Understanding Points, Lines and Planes 1.1 J A B C D E F G H I K Name 3 points that are: a. Collinear b. Coplanar c. Noncollinear d. Noncoplanar Name the intersection of the two planes.

Chapter 1 Understanding Points, Lines and Planes 1.1 Postulate or Axiom: an accepted statement of fact. Postulate 1-1: Through any two points there is exactly one line. Postulate 1-2: If two lines intersect, then they intersect in exactly one point. Postulate 1-3: If two planes intersect, then they intersect in exactly one line. Postulate 1-4: Through any three noncollinear points there is exactly one plane.

Chapter 1 Understanding Points, Lines and Planes 1.1 Use the diagram below… What is the intersection of planes … HGC and AED? Name a plane that contains pts E, G and F? ABC and GBC? A, D and H? HGF and ADC? B and C DCG and EFG? A and G AD and BF? GC and FG?

Chapter 1 Understanding Points, Lines and Planes 1.1 Segment: the part of a line consisting of two endpoints and all points between them. Segments are identified by the endpoints and a bar over the endpoint identifiers. Segment AB Endpoint A B

Chapter 1 Understanding Points, Lines and Planes 1.1 Ray: the part of the line consisting of one endpoint and all the points of the line on one side of the endpoint. Rays are identified by the endpoint and another point of the ray with a ‘single arrow’ bar over the points. Ray YX Endpoint X Y XY U M A X Name the ray with endpoint at point U and contains point X Name the ray with endpoint at point U and contains point M

Chapter 1 Understanding Points, Lines and Planes 1.1 M A X Is there a difference between MU and AX? Is there a difference between MU and MA? Is there a difference between AU and UA? What is special about rays AM and AU? Can you name another set of opposite rays?

Chapter 1 Measuring Segments 1.2 4 7 10 14 33 36 A B C D E F What is the distance from A to B? B to D? B to A? C to F? E to A?

Chapter 1 Measuring Segments 1.2 The number line and “distance”. Postulate 1-2-1: Ruler Postulate The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. A B a b The length of AB AB = coordinate of A coordinate of B

Chapter 1 Measuring Segments 1.2 Find which two of the segments XY, ZY, and ZW are congruent. Use the Ruler Postulate to find the length of each segment. XY = | –5 – (–1)| = | –4| = 4 ZY = | 2 – (–1)| = |3| = 3 ZW = | 2 – 6| = |–4| = 4 Because XY = ZW, XY ZW.

Chapter 1 Measuring Segments 1.2 Congruent versus equivalent … what is the difference? Congruent segments: two segments with the same length. The symbol for congruence is and not =. In figures congruent segments are denoted with tic marks. A D B C AB = CD

Chapter 1 Measuring Segments 1.2 Mr. Mack’s happy home The distance from Mr. Mack’s house to the Mellow Mushroom is 12 miles. If Mr. Rick’s house is 3 miles from the Mellow Mushroom how far does Mr. Mack live from Mr. Rick? If Mr. Rick’s house is 5 miles from the Mellow Mushroom how far does Mr. Mack live from Mr. Rick Mr. Rick’s house Mellow Mushroom

Chapter 1 Measuring Segments 1.2 Post. 1-2-2: Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. A B C G is between F and H, FG = 6, and FH = 11. Find GH. Draw a diagram representing the situation. F G H 6 11 FH = FG + GH Seg. Add. Postulate 11 = 6 + GH Substitute 6 for FG and 11 for FH.

Chapter 1 Measuring Segments 1.2 B C D E F Does AB + BD = AD BD + DF = BF No gaps…No overlaps BC + DF = BF DE+ BD = BE BD + CE = BE

Chapter 1 Measuring Segments 1.2 Mr. Mack’s happy home The distance from Mr. Mack’s house to the Mellow Mushroom is 12 miles. If Mr. Rick’s house is the midpoint between Mellow Mushroom and Mr. Mack’s house, how far does Mr. Mack live from Mr. Rick? Mr. Rick’s house Mellow Mushroom

Chapter 1 Measuring Segments 1.2 Midpoint: a point that divides a segments into two congruent segments. We say point B bisects segment AC A B C If AB = 25, find the value of AN and NB. M is the midpoint of RT. Find RM, MT, and RT.

Assignment 1.1(9): 13-34,38,40,42 1.2(17): 12,15-18,20-23,28,32,36-40