POINTS LINES AND PLANES BIG IDEA REASONING AND
POINTS, LINES AND PLANES • • BIG IDEA: REASONING AND PROOF ESSENTIAL UNDERSTANDINGS: Geometry is a mathematical system built on accepted facts, basic terms, and definitions. A postulate or axiom is an accepted statement of fact. MATHEMATICAL PRACTICE: Attend to precision
Getting Ready • Make the figure at the right with a pencil and a piece of paper. Is the figure possible with a straight arrow and a solid board? Explain.
Undefined terms • In Geometry, some words such as point, line and plane are undefined. Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry. Although you cannot define undefined terms, it is important to have a general description of their meaning. • A Point indicates a ________ and has _______ size. You represent a point by a ____ and name it by a _____ letter. • A Line is represented by a _______ path that extends in two ________ directions without ____ and has no _______. A line contains ________ many points. You represent a line by any _______ points or by a single _____ letter. • A Plane is represented by a _____ surface that extends without _____ and has no ________. A plane contains _______ many points. You represent a plane by a _____ letter or at least ______ points in the plane that do _______ lie on the same ______.
Defined terms • Collinear points: points that lie on the _____ line • Coplanar: points and lines that lie in the _____ plane • Segment: part of a _____ that consists of two _______ and all points ______ them. You represent the segment by its _____ endpoints. • Ray: part of a _____ that consists of ____ endpoint and all the points of the line on _____ side of the ______. You represent the ray by its ______ and another point with the order indicating the ray’s ______. • Opposite rays: two rays that ______ the same ______ and form a ______. You represent the opposite rays by their _______ endpoint and any other _____ on each ray.
EX: Name the parts of the diagram • a) Name 3 points that are coplanar. • b) Name 3 points that are collinear. • c) What are two other ways to name ? • d) What are two ways to name the plane? • e) What are two points that are not coplanar with points L, N and O? • f) Name 3 rays in the figure. • g) Which of the rays are opposite rays?
Draw it • EX: Draw three collinear points , with. Draw point. Draw line. Draw point between the endpoints of the line. Draw segment. Draw rays • Name the following: • a) 3 non collinear points • b) 2 rays which are not opposite rays • c) 2 line segments that are on the same line • d) the point of intersection of the lines
Postulate or Axiom: an accepted statement of fact • Postulates, like undefined terms, are basic building blocks of the logical system in Geometry. You will use logical reasoning to prove general concepts in this book. • Postulate 1 -1: Through any two points there is exactly _______ line. • Postulate 1 -2: If two distinct lines intersect, then they intersect in exactly ____ point. • Postulate 1 -3: If two distinct planes intersect, then they intersect in exactly one _____. • Postulate 1 -4: Through any three non collinear points there is exactly one _____.
EX: Name the intersection of each pair of planes or lines in the figure. • a) • b) • c) • d) • e)
Draw it • EX: Three lines that lie in the same plane, but two of the lines do not intersect with each other and the third line intersects with each of the other lines in a point. • EX: Two planes which do not intersect and a line which intersects each plane in a point.
1. 2 P. 13 9 – 39 X 3, 14; 44 – 47, 48 – 66 X 3, 52, 53, 64; 73 – 75, 78, 80, 90 – 96 EVENS 35 questions
- Slides: 10