Unit 1 Foundations of Geometry Points, Lines and Planes 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

Unit 1 Foundations of Geometry Points, Lines and Planes Using the figure to the right, How many other ways can you reference line m? A B C D E F m k How many ways can you reference line CE? Name a set of collinear points. Name noncollinear points Are points A and B collinear?

Unit 1 Foundations of Geometry Points, Lines and Planes 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.

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

Unit 1 Foundations of Geometry Points, Lines and Planes 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.

Unit 1 Foundations of Geometry Points, Lines and Planes Use the diagram below. What is the intersection of planes… HGC and plane AED? ABC and plane GBC? HGF and plane ADC? DCG and plane AEF? Name a line that is parallel to line AB. T or F…if two lines do not intersect then they are parallel? Name a line that is skew to line AB.

Unit 1 Foundations of Geometry Segments and Rays 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

Unit 1 Foundations of Geometry Segments and Rays 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

Unit 1 Foundations of Geometry Segments and Rays X Is there a difference between MU and AX? U M A X Is there a difference between MU and MA? U M A X

Unit 1 Foundations of Geometry Segments and Rays X Is there a difference between AU and UA? U M A X What is special about rays AM and AU? U M A X Can you name another set of opposite rays?

Unit 1 Foundations of Geometry Segments and Rays 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?

Unit 1 Foundations of Geometry Segments and Rays 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

Unit 1 Foundations of Geometry Segments and Rays 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.

Unit 1 Foundations of Geometry Segments and Rays 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

Unit 1 Foundations of Geometry Segments and Rays 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

Unit 1 Foundations of Geometry Segments and Rays 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.

Unit 1 Foundations of Geometry Segments and Rays 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

Unit 1 Foundations of Geometry Segments and Rays 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):13,15,17,22-27,31-34,38,39,41,46 1.2(17):11,15,17,18,21,23,27,31,33,39,43