PRE-GEOMETRY “ Thinking about thinking”
BASIC CONCEPTS <ul><li>Geometry is being defined as visual mathematics. </li></ul><ul><li>Geometry of today was written do...
<ul><li>Points, lines, planes and space are building blocks of geometry. </li></ul><ul><li>We are going to see a lot of di...
<ul><li>In geometry, it doesn’t get basic much more then point. </li></ul><ul><li>Point: point is a dot which has no lengt...
<ul><li>Line: a line is a straight arrangement of points. Line has no width and thickness but its length extends infinity ...
l . . B A AB
<ul><li>Intersecting lines: two lines those have at least one common point are called intersecting lines. Common point is ...
<ul><li>Parallel lines: two coplanar lines those don’t have any intersection (common point) are called parallel lines. We ...
<ul><li>Coincident lines: two lines are coincident if each one contains all the points of the other one. </li></ul>Basic c...
<ul><li>Collinear points: points which lie on the same line are called collinear points. </li></ul>Basic concepts . B A . ...
<ul><li>Ray: a ray lies like a line except begins from one point and extends in one direction to infinity. Just like rays ...
<ul><li>Segment (line segment): a segment is a part of a line between two different points. We denote segment with a solid...
<ul><li>A ray has one end point, </li></ul><ul><li>A segment has two end points, </li></ul><ul><li>A line has no end point...
<ul><li>Plane: think about a flat surface area like a table which extends infinitely in all directions is called a plane. ...
<ul><li>Coplanar points: points on the same plane are called coplanar points. </li></ul>Basic concepts P . . . . . A B C E D
<ul><li>Coplanar lines: lines on the same plane are called coplanar lines. </li></ul>Basic concepts P
<ul><li>Skew lines: two lines those non-coplanar and not intersecting are called skew lines. </li></ul>Basic concepts l m
<ul><li>Space: set of all points is called space. Points, lines, planes are all somewhere in space. </li></ul>Basic concepts
Angles  <ul><li>Angle: an angle is two rays or segments those share the same endpoint.  </li></ul>
Interior and exterior region: <ul><li>The region between the sides and contains angle is called interior region. </li></ul...
Measuring angles: <ul><li>One unit of measurement of an angle is the  degree.  It is 1/360 of a full revolution. </li></ul...
Protractor: circular protractor
Protractor: semi-circular protractor
How to measure an angle using protractor? <ul><li>place the centre of the protractor on the vertex of the angle </li></ul>...
60°
How to construct an angle using protractor? <ul><li>Draw a straight line. </li></ul><ul><li>Put a dot at one end of the li...
130°
Types of angles <ul><li>Angles can be classified according to their size. </li></ul><ul><li>Acute angle: An angle measures...
Types of angles <ul><li>Right angle: A  right  angle is an angle that equals exactly 90°. </li></ul>
Types of angles <ul><li>Obtuse angle: An  obtuse  angle is greater than 90° but less than 180°. </li></ul>
Types of angles <ul><li>Straight angle: A  straight  angle equals exactly 180°. </li></ul>
Types of angles <ul><li>Reflex angle: A  reflex  angle is greater than 180° but less than 360°. </li></ul>
Types of angles <ul><li>Revolution or Complete angle: A  revolution , or a  complete  is  an angle of 360° (a full circle)...
 
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Pre geometry

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Pre geometry

  1. 1. PRE-GEOMETRY “ Thinking about thinking”
  2. 2. BASIC CONCEPTS <ul><li>Geometry is being defined as visual mathematics. </li></ul><ul><li>Geometry of today was written down and discovered in ancient time guys like Pythagoras and Euclid. </li></ul><ul><li>Actually today's geometry in schools is known Euclidian geometry. </li></ul>
  3. 3. <ul><li>Points, lines, planes and space are building blocks of geometry. </li></ul><ul><li>We are going to see a lot of different shapes and how they are put together then we take a look relationships between one shape and another. </li></ul>Basic concepts
  4. 4. <ul><li>In geometry, it doesn’t get basic much more then point. </li></ul><ul><li>Point: point is a dot which has no length, width, and thickness. It is just a place holder. We use capital letters to represent points such as A, B, X, W, …. </li></ul>Basic concepts
  5. 5. <ul><li>Line: a line is a straight arrangement of points. Line has no width and thickness but its length extends infinity in two directions. Usually we name lines with lower case italic letters such as l, d, m, n, … or by naming two points and topping them with two-arrow symbol. </li></ul>Basic concepts
  6. 6. l . . B A AB
  7. 7. <ul><li>Intersecting lines: two lines those have at least one common point are called intersecting lines. Common point is called intersection point. </li></ul>Basic concepts l m
  8. 8. <ul><li>Parallel lines: two coplanar lines those don’t have any intersection (common point) are called parallel lines. We denote parallelism with symbol of || </li></ul>Basic concepts l m m || l
  9. 9. <ul><li>Coincident lines: two lines are coincident if each one contains all the points of the other one. </li></ul>Basic concepts l m
  10. 10. <ul><li>Collinear points: points which lie on the same line are called collinear points. </li></ul>Basic concepts . B A . . . C D
  11. 11. <ul><li>Ray: a ray lies like a line except begins from one point and extends in one direction to infinity. Just like rays of the sun. We denote ray using single arrow at the top of points. </li></ul>Basic concepts B A . . AB
  12. 12. <ul><li>Segment (line segment): a segment is a part of a line between two different points. We denote segment with a solid line at the top of points. </li></ul>Basic concepts B A . . AB
  13. 13. <ul><li>A ray has one end point, </li></ul><ul><li>A segment has two end points, </li></ul><ul><li>A line has no end points. </li></ul>Basic concepts
  14. 14. <ul><li>Plane: think about a flat surface area like a table which extends infinitely in all directions is called a plane. A plane has length and width but no thickness. We denote plane with ( ). Example: (P), (O), (R),…. </li></ul>Basic concepts P
  15. 15. <ul><li>Coplanar points: points on the same plane are called coplanar points. </li></ul>Basic concepts P . . . . . A B C E D
  16. 16. <ul><li>Coplanar lines: lines on the same plane are called coplanar lines. </li></ul>Basic concepts P
  17. 17. <ul><li>Skew lines: two lines those non-coplanar and not intersecting are called skew lines. </li></ul>Basic concepts l m
  18. 18. <ul><li>Space: set of all points is called space. Points, lines, planes are all somewhere in space. </li></ul>Basic concepts
  19. 19. Angles <ul><li>Angle: an angle is two rays or segments those share the same endpoint. </li></ul>
  20. 20. Interior and exterior region: <ul><li>The region between the sides and contains angle is called interior region. </li></ul><ul><li>The region which doesn’t contain angle is called exterior region. </li></ul>
  21. 21. Measuring angles: <ul><li>One unit of measurement of an angle is the degree. It is 1/360 of a full revolution. </li></ul><ul><li>We can use a protractor to measure angles in degrees. </li></ul>
  22. 22. Protractor: circular protractor
  23. 23. Protractor: semi-circular protractor
  24. 24. How to measure an angle using protractor? <ul><li>place the centre of the protractor on the vertex of the angle </li></ul><ul><li>match the 0° horizontal centre line with one of the arms of the angle </li></ul><ul><li>read the size of the angle, indicated by the other arm. </li></ul>
  25. 25. 60°
  26. 26. How to construct an angle using protractor? <ul><li>Draw a straight line. </li></ul><ul><li>Put a dot at one end of the line. (The line represents one of the arms and the dot represents the vertex of the angle.) Place the protractor so that its centre is on the vertex and 0° is on the baseline. </li></ul><ul><li>Find the required angle on the scale and mark a small dot at the edge of the protractor. </li></ul><ul><li>Join the small dot with the vertex to form the second arm of the angle. </li></ul><ul><li>Label the angle. </li></ul>
  27. 27. 130°
  28. 28. Types of angles <ul><li>Angles can be classified according to their size. </li></ul><ul><li>Acute angle: An angle measures bigger than 0° less than 90° is called acute angle. </li></ul>
  29. 29. Types of angles <ul><li>Right angle: A right angle is an angle that equals exactly 90°. </li></ul>
  30. 30. Types of angles <ul><li>Obtuse angle: An obtuse angle is greater than 90° but less than 180°. </li></ul>
  31. 31. Types of angles <ul><li>Straight angle: A straight angle equals exactly 180°. </li></ul>
  32. 32. Types of angles <ul><li>Reflex angle: A reflex angle is greater than 180° but less than 360°. </li></ul>
  33. 33. Types of angles <ul><li>Revolution or Complete angle: A revolution , or a complete is an angle of 360° (a full circle). </li></ul>

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