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Defined and Undefined Terms in Geometry.pptx
- 1. BASIC UNDEFINED TERMS INGEOMETRY (Point, Line, and Plane)
- 2. OBJECTIVES: Describe the ideasof point, line, and plane Identify real-life representations of point, line, and plane Differentiate collinear points and noncollinear points Distinguish coplanar lines from non-coplanar lines
- 3. What do theylike? Have you ever watched the stars at night?
- 4. Stars during thenight look like DOTS. A DOT suggests the idea of one of the basic undefined terms in Geometry which is the POINT. Remember: We cannot define a point. We can just describe it.
- 5. NAME GRAPHICAL REPRESENTATION SYMBOL DESCRIPTION point A, point G, and point M G M A A G M Apoint has no length, width, or height. It indicates a position. Table 1
- 6. Consider points Gand M. If we will connect this two points, it will introduce us another basic undefined term - the LINE. G M GM read as line GM or MG read as line MG
- 7. NAME GRAPHICAL REPRESENTATION SYMBOL DESCRIPTION line CD and lineXY C D m Y X n CD, DC, or line m XY, YX, or line n A line has no width nor thickness but it has infinite length Table 2
- 8. A B C D Points Aand B are collinear points. Points C and D are also collinear points. Why are they called collinear points? ______________________________________ ____________________________________ ___________________ F E H G Points E and G are noncollinear points. Points E and H, points F and G, and points F and H are also noncollinear. Why are they called noncollinear points? _________________________________________ ______________________________________ _______________________
- 9. A B C D Points Aand B are collinear points. Points C and D are also collinear points. Why are they called collinear points? They are called collinear point because they lie on the same line. F E H G Points E and G are noncollinear points. Points E and H, points F and G, and points F and H are also noncollinear. Why are they called noncollinear points? They are called noncollinear because they DO NOT lie on the same line.
- 10. A set ofthree noncollinear points determines the third basic undefined term in geometry. Consider the figure. Noncollinear points P, Q, and R enclosed by a four-sided figure gives us plane PQR. What is a plane? P R Q
- 11. NAME GRAPHICAL REPRESENTATION SYMBOL DESCRIPTION Plane Q, Plane ABC, Plane BCA,or Plane CAB A B C Q ABC, BCA, CAB, or Q A plane has an infinite width and length but has no thickness. Table 3
- 12. Coplanar and Non-coplanarLines Lines that lie on the same plane are called coplanar lines. Lines that do not lie on the same plane are called non-coplanar lines. Similarly: Points that lie on the same plane are called coplanar points. Points that do not lie on the same plane are called non-coplanar points.
- 13.
- 14. Activity 1: In agroup of five, identify representations of points, lines, and planes that you can see around the campus. List as many as you can on your activity sheet.
- 15. Group Number: Members: Date: Activity 1:REAL-LIFE REPRESENTATIONS OF UNDEFINED TERMS IN GEOMETRY List real-life representations of points on the first column, of lines on the second column, and of planes on the third column. POINTS LINES PLANES
- 16. Activity 2: Identify theundefined term represented by each of the following physical examples.
- 17. 1. Edge ofa box kite line
- 18.
- 19. 3. Tip ofa pen point
- 20. 4. Edge ofa table line
- 21. 5. Face ofa frame plane
- 22.
- 23. 6. Cover ofa book plane
- 24.
- 25.
- 26. 9. Crease ofa paper line
- 27. 10. Tip ofa leaf point
- 28. Activity 3: Identify whetherthe given points are collinear (CL), noncollinear (NC), coplanar (CP), or non- coplanar (NP). Put a check (/)under the proper column. CL NC CP NP __ __ __ __ 1. Points G and P __ __ __ __ 2. Points F and J __ __ __ __ 3. Points F and I __ __ __ __ 4. Points C and E E H G J P C I F
- 29. Activity 3: (continuation) E H GJ P C I F CL NC CP NP __ __ __ __ 5. Points G and H __ __ __ __ 6. Points E and D __ __ __ __ 7. Points J and J __ __ __ __ 8. Points H and F __ __ __ __ 9. Points I and J __ __ __ __ 10. Points C and I
- 30. Topic: BASIC UNDEFINEDTERMS IN GEOMETRY References: 1. Geometry by E. Mapile 2. Geometry in the real world by K. D. Romero 3. Geometry by A. A. Sarmiento & R. L. Villar 4. Geometry(a work text in Math III) by V. C. Tafalla, et al. 5. Secondary Mathematics Learning Competencies (Mathematics III) A. 1.1 – 1.5 Prepared by: MS. DIVINA JOY A. VENTURA MA 202 (Instructional Materials Development with Computer Literacy) Summer; School Year 2009 - 2010