Definitions

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

2. 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.

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

4. M B C A Plane • _________________________ • _____________________ • _________________________ • _________________________ • _________________________ Plane ABC or plane M _________________________– Points that lie on the same line _________________________– Points that do not lie on the same line _________________________– Points that lie on the same plane _________________________– Points that do not lie on the same plane

5. A B G H F I C D E Why do we need to use three non- collinear points when naming a plane? 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?

6. Line segment or segment: Q R Symbol: A B C D ______________________________________ • Has one dimension - length • Is part of a line • Has endpoints – a beginning and an end • Named using its endpoints Name each of the segments in the following figure:

7. F B Symbol: What are all the ways that the whole ray can be named? A R M Y Is AM the same as RM? 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 No – different starting point

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

9. Line 1 Line 2 A B C D E Plane DCB and Plane CBF create ____ Plane DCG and Plane EFG create____ F H G Intersection • 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.

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

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

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