Chapter 1: Tools of Geometry 1- 3 Points, Lines, and Planes

Objectives, student will be able: 1. To understand basic terms of geometry. 2. To understand basic postulates of geometry. CW/HW: pgs. 19-21 #’s 2 – 48 Even

Points How to sketch: B A How to label: C A * dots * Use capital printed letters. * Never label two points with the same name (in the same sketch). *Think of points as location markers. *Points are zero dimensional.

Collinear Points Definition: Collinear points are points that lie on the same line. (The line does not have to be visible.) collinear non-collinear

NEVER n Lines ? ? ? How to sketch: ? How to label: ? * must have arrows at both ends ? ? ? How to label: ? ? ? (Two methods) Possible Names: 1- small “script” letter 2- any two points on the line

Planes How to sketch: How to label: M * horizontal * vertical P N horizontal “edges” M * horizontal * vertical P N * other How to label: vertical “edges” (Two methods) 1- capital “script” letter 2- any three points on the plane Think of a plane as a flat surface that has no thickness A plane contains an infinite many lines and extends without end

Planes How to label: #2- any three points on the plane

Planes How to label: any three points on the plane How many planes do you see?

Planes How to label: any three (or more) points on the plane How many planes do you see? plane ABCD plane ABC plane BCD plane CDA plane DAB etc.

Planes How to label: any three (or more) points on the plane How many planes do you see? plane EFGH plane EFG plane FGH plane GHE plane HEF etc.

Planes How to label: any three (or more) points on the plane How many planes do you see? plane AEHD plane EHD plane HDA plane DAE plane AEH etc.

Planes How to label: any three (or more) points on the plane How many planes do you see? plane BFGC plane BFG plane FGC plane GCB plane CBF etc.

Planes How to label: any three (or more) points on the plane How many planes do you see? plane ABFE plane ABF plane BFE plane FEA plane EAB etc.

Planes How to label: any three (or more) points on the plane How many planes do you see? plane DCGH plane DCG plane CGH plane GHD plane HDC etc.

Planes How to label: any three (or more) points on the plane Any three points determine a plane! plane AFGD plane ACH plane ACGE plane AGF plane BDG etc.

Coplanar Definition: Coplanar objects (points or lines) are objects that lie on the same plane. (The plane does not have to be visible.) Are they coplanar? ABC ? yes ABCF ? NO HGFE ? yes EHCB ? yes AGF ? yes CBFH ? NO

Postulate or Axiom A postulate or axiom is an accepted statement as fact. Postulate and Axioms have no formal proof they exist or are true Many mathematicians do years of research trying to prove postulates or axioms true. Postulates and axioms that are proven true are known as Theorems.

Postulate 1-1 Through any two points there is exactly one line. Line t is the only line that passes through points A and B.

Postulate 1-2 If two lines intersect they intersect in exactly one point and intersect at C.

Postulate 1-3 If two planes intersect, then they intersect in exactly one line. Plane RST and Plane STW Intersect in .

Postulate 1-4 Through any three noncollinear points there is exactly one plane. “Think of a tripod”

Space Space – the set of all points Total space in zero dimensions is a point. Total space in one dimension is a line. Total space in two dimensions is a plane Total space in three dimensions infinite in all diections