DEFINED AND UNDEFINED TERMS IN GEOMETRY.pptx

For educational purposes only.

1. Undefined and Defined Terms of Geometry Name of Teacher Subject

2. OBJECTIVES After going through this lesson, you are expected to: 1. Determine the different basic undefined and defined terms of geometry; 2. Name the different basic geometric figures appropriately; and 3. Represent point, line, and plane using concrete pictorial models

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4. 4 What did the architect use in designing the building?

5. 5 What did the architect use in designing the building?

6. 6 What did the architect use in designing the building?

7. 7 What did he consider in creating attractive patterns?

8. 8 What did he consider in creating attractive patterns?

9. 9 What did he consider in creating attractive patterns?

10. 10 What is Geometry?

11. 11 What is Geometry?

12. 12 Geometry is a branch of mathematics that deals with the study of shapes, sizes, figures, spaces, and all quantities related to the things you see on Earth.

13. 13 Why do we do Geometry?

14. 14 We do geometry to discover patterns , find areas, volumes, lengths and angles , and better understand the world around us .

15. 15 The word geometry is a conglomeration of the Greek words “geo” and “ metron ”. Geo : means “Earth ” Metron : means “measurement”

16. 16 In short, geometry is the mathematical study of Earth measurement .

17. Geometry is grounded on the idea that everything around us is made up of smaller geometric units called points , lines , and planes .

18. 18 Euclid of Alexandria, Egypt The Father of Geometry

19. Points , lines , and planes are collectively called UNDEFINED TERMS. 19 because of the obvious idea that it is not possible to define them formally

20. 20 Students, close your eyes and imagine the stars in the sky at night. Then open your eyes how do the stars in the sky look like?

21. POINT Has NO part. Has position but with NO spatial magnitude, size, or dimension. Has NO width. Has NO thickness. Can be represented by a small dot on paper using the tip of the pencil. Locations of places on a map are also an example of points.

22. 22 These points are said “Point A,” “Point L”, and “Point F.” Points are labeled with a CAPITAL letter.

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24. 24 LINE Is a geometric figure which has NO width. Has NO thickness. Is a geometric figure which has NO width. Extends indefinitely in opposite directions. Can be imagined to be a very long pencil or rope where the starting point and the ending point cannot be seen.

25. 25 Line PQ Line g A line, like a point, does not take up space. It has direction, location and is always straight. Lines are one-dimensional because they only have length (no width). A line can be named or identified using any two points on that line or with a lower-case, italicized letter.

26. PLANE Is a surface which lies evenly with straight lines on itself. Is a two-dimensional (2-D) figure that HAS length and width. Has NO thickness. Some physical models of a plane include wall, floor, and window.

27. Plane ABC Think of a plane as a huge sheet of paper that goes on forever. Planes are two-dimensional because they have a length and a width. A plane can be classified by any three points in the plane.

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29. 1. COLLINEAR points - three or more points that lie on a straight line. 30 Some preliminary DEFINED TERMS in geometry: Obviously, two points are always collinear because they determine a line.

30. Where do points I, R and S lie? 31 How about point H, is point H collinear with the other three points? Why?

31. 2. COPLANAR points - three or more points lie on the same plane. 32 Some preliminary DEFINED TERMS in geometry:

32. Where can you locate point K, L, and M? 33 When points lie on the same plane, how will you describe them? Describe point N, is point N coplanar with the other three points?

33. 3. INTERSECTION of two lines : refers to the point common to both lines, that is, the point that can be found on both lines. 34 Some preliminary DEFINED TERMS in geometry:

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35. 36 Are you ready?

36. 37 Corner of a room

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38. Cable Wire 39

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40. Board 41

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42. Cover of a Book 43

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44. 45 Tip of a pencil

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46. 20XX presentation title 47 Floor

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48. 49 Floor

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50. 51 Edge of a building

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52. 53 Skipping rope

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54. 55 Retina of an eye

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56. 57 Give your own example

57. 58 Give your own example

58. 59 Illustrate Me! 1. Illustrate the intersection of two lines. What is their intersection? Label the lines and the intersection. 2. Illustrate intersecting line and plane. What is the intersection? Label the figure. 3. Illustrate intersecting line and plane. What is the intersection? Label the figure.

59. 60 Illustrate Me! 1. Illustrate the intersection of two lines. What is their intersection? Label the lines and the intersection. 2. Illustrate intersecting line and plane. What is the intersection? Label the figure. 3. Illustrate intersecting line and plane. What is the intersection? Label the figure.

60. 61 Let us Play: tic tac toe Two players will compete. The first who can make five consecutive points in a line will be the winner. First round put all your dots on the plane. Block the way of your opponent and aim to put all your dots on a line. If there’s no five consecutive dots formed, move your dots with the same goal, one step at a time. Be wise to win!

61. 62 Let us Play: tic tac toe Two players will compete. The first who can make five consecutive points in a line will be the winner. First round put all your dots on the plane. Block the way of your opponent and aim to put all your dots on a line. If there’s no five consecutive dots formed, move your dots with the same goal, one step at a time. Be wise to win!

62. 63 • A point is named using a capital letter. • A line is named using two capital letters representing any two points that lie on the line or using a lowercase script letter. The line notation using two points also includes a double-headed arrow ( ) above of the two capital letters. A plane is named using a single script uppercase letter or using any three points on the plane that do not lie on a straight line, in no specific order.

63. 64 COLLINEAR points - three or more points that lie on a straight line. Obviously, two points are always collinear because they determine a line. COPLANAR points - three or more points lie on the same plane. INTERSECTION of two lines : refers to the point common to both lines, that is, the point that can be found on both lines.

64. A. Name me! Identify what is asked on the following: 1. It is a flat surface that extends infinitely in all directions. 2. Points that lie on the same line. 3. It is a specific location in space that has no dimensions. 4. Points that lie on the same plane. 5. It is of infinite length, but it is no width and no thickness. 65 GROUP A:

65. B. Tell whether each represents a point, a line or a plane. 1. Your desktop 2. The surface of the page of a notebook. 3. The string on a guitar. 4. The ceiling of a room. 5. A broomstick. 6. Electric wire. 7. The floor. 8. A hair strand. 9. A rope. 10. A needle point. 66 GROUP B:

66. C . Give the appropriate name of the following geometric figures. 67 GROUP C:

67. D. TRUE or FALSE. Write T if the statement is true. If false, write F. 20XX presentation title 68 GROUP D:

68. 69 ASSIGNMENT   Subset of a line. Segment addition postulate.

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