Definitions Goals Understand and use the basic undefined and defined terms in geometry Sketch the intersection of lines and planes Academic Geometry: Chapter 1

Conjecture – an unproven statement that is based on observations _________________– process of looking for patterns and making conjectures To prove a conjecture is ______ – you must prove that it is true for ____ cases. To prove a conjecture is ______ – you must prove it is false for just ____ case. Example: Conjecture: If you are taking geometry, then you must be a sophomore True or False.____________________ _______________ – an example that shows a conjecture is false.

Point: Has no dimension Represents a location in space Represented by a small dot Named using a capital letter A Point A Line: Has one dimension - length Extends infinitely in opposite directions Named using two points on the line or scripted letter BLUE Name the following line as many ways as possible: AB c Symbol: Or line c

Plane _________________________ _____________________ _________________________ A B C M Plane ABC or plane M __________________ _______ – Points that lie on the same line __________________ _______ – Points that lie on the same plane _______________________ __ – Points that do not lie on the same plane ________________________ _ – Points that do not lie on the same line

Why do we need to use three non- collinear points when naming a plane? AB C D E F GH I Place your pencil on Plane ABH. Top of the box. Place your pencil on Plane BHC. Right side of the box. Place your pencil on Plane FGH. Is it the top or the front? Place your pencil on Plane HID. Is it the front or the right side?

Line segment or segment: Has one dimension - length Is part of a line Has endpoints – a beginning and an end Named using its endpoints QR Symbol: ABCD Name each of the segments in the following figure: ______________________________________

Ray Has one dimension - length Is part of a line Has one endpoint Extends infinitely in one direction Named using its endpoint first and then another point on the ray FB Symbol: AYRM What are all the ways that the whole ray can be named? Is AM the same as RM?No – different starting point

Opposite Rays Rays which share the same endpoint and extend in opposite directions Any two opposite rays are collinear ABC BA and BC are opposite rays Are BC and CB opposite rays? No – different starting points Intersect Two or more geometric figures intersect if they have one or more points in common Where figures come together

Line 1 Line 2 Intersection B D A F C H E G What is created by the intersection of two lines? _______ What is created when two planes intersect? ______ Name two planes that intersect and the line that their intersection makes. Plane DCB and Plane CBF create ____ Plane DCG and Plane EFG create____

Intersection (continued) B D A F C H E G What is created when three planes intersect each other? Is it possible for two planes not to intersect? If yes, name two that do not intersect. Plane EFG and Plane ABC Plane ADH and Plane FGC Planes ABC, BCF, and GDH intersect at…? __________

B D A F C H E G Are points A, B, and G on the same plane? ______

B D A F C H E G Parallel Lines:_________________________ Skew Lines: _________________________