WARMUP • (10, -4) AND (6, 0) – FIND THE DISTANCE BETWEEN THE 2 POINTS. – FIND THE SLOPE BETWEEN THESE 2 POINTS. – FIND THE MIDPOINT.
POINTS, LINES, AND PLANES Agenda: • Warmup • Points, Lines, and Planes Notes • Quick Check • Intersection Notes HW: worksheet Learning Target: I can identify points, lines and planes
Geometry: the study of points, lines and planes as they exist in space. These building blocks for Geometry are accepted as intuitive ideas and are not defined. Instead, they are described by their characteristics and are also used in the definitions of other terms. Approximate examples can be seen in our every day lives.
Point – the simplest figure in geometry. A point has no size and no dimension; it represents one position in space. Notation: Points are named by capital letters. Example: Points A and B A B
A series of points can create a line. A line extends in two directions without ending. A line has only one dimension. Notation: Lines can be denoted by using two points that lie on the line or by using a lower case letter. B AB or BA A Line m m
A plane can be visualized by looking at the floor or a wall. It is a two dimensional figure that extends in both dimensions forever and has no thickness. There are no edges to a plane. Notation: A plane is either named by one capital letter (like a point!) or by at least three points (but no more than four points) that lie in the plane. B D C A Plane M Plane ABC or Plane ABCD
Where have you seen points, lines, and planes before in math class? The Coordinate Plane Plotting Points. Ex. (-2, 4) Graphing Lines in slope-intercept form. Ex. y = 2x + 2
Space is the set of all points. Space has three dimensions.
Collinear Points are points that lie on the same line. Are A and B E collinear points? A C Yes!! In fact any D two points are collinear. We B can always draw exactly one line between two A, C, and D are collinear points. given points. B, C, and D are noncollinear points.
Coplanar Points are points that lie on the same plane. K C A J B G H D A, B, C, and D are coplanar points. K, J, G, and H are noncoplanar points.
The intersection of two figures is the set of points The symbol for that are in both “to intersect” is figures. If two lines If two planes intersect, then they intersect, then they intersect at a point. intersect at a line. B q M N p r line q line r at point B . plane M plane N at line p.
Check for Understanding: CW Textbook (pages 17-18) Exercises pg. 17 #’s (3 -8, 19-26) all
Intersection Examples: G F E D H C A B DF. 1. Plane GEDF Plane DFBC at 2. Plane EDBA Plane GEAH at EA. Point D. 3. DB DF at Point E. 4. EF EA at
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