Chapter 1 2 Points Lines And Planes GEOMETRY

Chapter 1. 2 Points, Lines, And Planes GEOMETRY

A B t

Collinear: Noncollinear: • Three or more points on a line. • Points do not form a line. ● ● A B C B ● ● A C

Ex. 1) Identify Collinear Points a) Are the following points collinear? A, E, C G, F, B D, E, A b) Name line m in three other ways c) Name line l in three other ways

PLANE • • • Flat Surface/No Thickness Infinite Number of Points and Lines Extends Without End • Any 3 Noncollinear Points ALWAYS Make a Plane • Name a Plane • A Capital Letter or • At Least 3 of its Noncollinear Points Plane RST or Plane X R. S. T. X

Ex. 2) Name the Plane A B D H b) The Top C E c) The Front F G a) The Bottom d) The Back e) The Left Side f) The Right Side

COPLANAR Lines or points in the same plane. R. S. T. X

Through any 2 points there is exactly one line. B A t Line t is the only line that passes through points A and B. Postulate 1 -1 Two lines intersect in exactly one point. ● m Lines m and n intersect at point P. P n Postulate 1 - 2

A line and a plane intersect, in exactly one point.

Postulate 1 -3 Two planes intersect, in exactly one line. Plane ABC and Plane D intersect at line t. ●A ●B ●C D t

Picture this cube as having Planes M, L and P. They intersect in 3 separate lines. M P L

Ex. 3) Name the intersection of Planes ABC & BFG A B D C E H Name two planes that intersect the given line. F G

Postulate 1 -4 Through any 3 noncollinear points there is exactly one plane. A Can you name sets of noncollinear points? B D C E H F G

A Find Planes: ABC HEF BCG ADG B D C E H F G

Ex. 4) A. Shade the plane containing points A, E, F A D B. Name another point in Plane EHG C. Is point F coplanar with plane DCG? B C E H F G