1-3: Points, Lines, and Planes

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Presentation transcript:

1-3: Points, Lines, and Planes Geometry

Objectives/Assignment: Be able to understand basic terms and postulates of geometry.

point - ______________________ ______________________ Location with no size, represented by a small dot, named by a capital letter A _________________________ a geometric figure consists of a set of points space - ______________________ a boundless, 3-D set of all points

line - ________________________ ________________________ series of points that extends in two opposite directions without end m Q PQ line PQ P line m QP Points that lie in the same line are _______________. collinear points (PQ are collinear)

X, Y, and Z are not collinear X, W, and Z are not collinear In the figure below, name 3 points that are collinear and 3 points that are not collinear (noncollinear). X Z W Y Y, Z, and W are collinear Why are arrowheads on the lines? X, Y, and Z are not collinear X, W, and Z are not collinear

__________________________________ Plot __________________________________ __________________________________ A(0, -4), B (2, 2), and C(3, 5) on a coordinate plane. C B A _____________________________________________ What are your observations? Points A, B, and C are collinear.

a flat surface that has no thickness; plane - _______________________ _______________________ _______________________ _______________________ contains many lines and extends infinitely far in the direction of its lines. R B C A Plane R Plane ABC *A, B, C are noncollinear points Points and lines in the same plane are ___________. coplanar

1. Name two different planes that contain points C and G. B F D H A E J 1. Name two different planes that contain points C and G. plane BCG, plane DCG 2. Name the intersection of plane AED and plane HEG. HE 3. How many planes contain the points A, F, and H? 1 (3 noncollinear points)

Are points B, C, and E coplanar? G B F D H A E J Are points B, C, and E coplanar?

postulate - _____________________ _____________________ or axiom; an accepted statement of fact Postulate 1-1_________________________ ______________________________ Through any two points, there is exactly one line. m B A

______________________________ 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. P Plane PQR and Plane QRS intersect at QR S Q R

______________________________ Postulate 1-4 ___________________________ ______________________________ Through any 3 noncollinear points there is exactly one plane. B A C Plane ABC

Page 19 #1-10 m A G n D C F B E Are the 3 points collinear? If so name the line on which they lie. A, D, E B, C, D No Yes – BC, BD, CD, CB, DB, BF, CF, DF, FD, FB, FC, DC, n

Page 20 # 11-16 Name the plane represented by each surface of the box. Top EGH

Page 20 #17-37 Name the intersection of each pair of planes. X W U V T S Q R Name the intersection of each pair of planes. Planes QRS and RSW RS

ON YOUR OWN Due tomorrow!!! Complete page 20-21 (evens only) 38-42 46-60 68-72