1. http://mathematics-teacher.com David Vundi Mathematics Teacher http://mathematics-teacher.com Identify Points, Lines, and Planes GEOMETRY

2. http://mathematics-teacher.com David Vundi Objective 2  Understand and use the basic undefined terms and defined terms of geometry.  Sketch the intersections of lines and planes.

3. http://mathematics-teacher.com David Vundi Lines A B Line AB p or Line p H I Line HI M N Line MN is VERTICAL is HORIZONTAL How do we call this line? What about this other?

4. http://mathematics-teacher.com David Vundi Lines C F Line CD m Line m ? D E How many different ways can we call Line CE Line CF Line DE Line DF Line EF Line DC Line EC Line FC Can you figure out other names? OR IN GENERAL A LINE IS NAMED BY TWO POINTS.

5. http://mathematics-teacher.com David Vundi Segments D E If we have line DE and we take one part of the line

6. http://mathematics-teacher.com David Vundi Segments D E If we have line DE D E and we take one part of the linethen this part is called: LINE SEGMENT DE Can you name the different line segments in the following line: S TU ST SU TU TS US UT SEGMENTS: OR

7. http://mathematics-teacher.com David Vundi Rays A B This is RAY AB What are the differences between a Line, a Line Segment and a Ray? The line is infinite and never ends at either side. The line segment has two endpoints. The ray has on one side one endpoint at the other side it never ends it goes on to infinite. M N D E A B What do they have in common? They all made up of points; They all are straight; They are named using TWO POINTS.

8. http://mathematics-teacher.com David Vundi Collinear and Non collinear Points C F D E Points C, D, E and F: are they COLLINEAR? Yes, they are COLLINEAR because they lie in the same line No, they are NONCOLLINEAR because they don’t lie in the same line. Are points A, B, C, and D collinear? A C B D

9. http://mathematics-teacher.com David Vundi Can you explain where the following two lines intersect? l m A B C D E They INTERSECT at point E. Can they intersect at other point? NO

10. http://mathematics-teacher.com David Vundi Planes M A C D B The figure above represents a PLANE, which is a flat surface that has no end at any of the sides. What examples can you give of objects lying in a PLANE? This is PLANE M PLANE ADC PLANE BDC PLANE ABD In general a Plane can be named using three non-collinear points. The wall of a house Top of the table The lid of a shoebox. The ground of a football field.

11. P M A B l m n Can you describe the INTERSECTION of planes M and P ? Planes M and P intersect at line AB. PLANES ALWAYS INTERSECT AT A LINE. Where do lines m and l intersect? They intersect at point B. LINES ALWAYS INTERSECT AT A POINT. Where do lines n and l intersect? At point A.

12. Are Points L, K, and M COPLANAR? Yes, they are COPLANAR because they LIE ON THE SAME PLANE P. Is point H, coplanar with points L, K, and M? P Q A B L K M H C No, because it lies on plane Q and points L, K, and M are in different plane, on plane P. NON-COPLANAR points are points that lie in different planes. D

13. P Q A B C D On what planes does point C lie?

14. P Q A B C On what planes does point C lies? On planes P and Q. D

15. On what planes does point D lie? P Q A B C D

16. It only lies on plane Q. P Q A C B D

17. P Q A C B D On what plane is line k lying? Since points B and D lie on plane Q then line k lies on its entirety on plane Q k

18. http://mathematics-teacher.com David Vundi SUMMARIZING FINDINGS: 18 Through any two points there is exactly one line. Through any three points not on the same line there is exactly one plane or through any three points non-collinear there is one plane. A line contains at least two points. A plane contains at least three points not on the same line. A plane contains at least three non-collinear points. If two points lie in a plane, the entire line containing those points lies in that plane.

19. http://mathematics-teacher.com David Vundi Enjoy your Life Everyday www.david-s.org