Lines and angles


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Lines and angles

  1. 1. Lines And Angles<br />By<br />Soumya Sankar Modak<br />Class :- IX – D<br />Roll Number :- 31<br />
  2. 2. Lines and angles<br />Introduction<br />Angles In Daily Life<br />Basic Terms And Definitions<br />Points<br />Intersecting Lines And Non Intersecting Lines<br />Perpendicular Lines<br />Angles<br />Parallel Lines And A Transversal<br />
  3. 3. Introduction<br />In math geometry the lines and angles are important tools. If any object in ideal, that is called as line and it is represented as straight curve. <br />The angle is related with line that is the cross-section of two-line is create the angle and that intersection point is called as vertex. Here we see about types of line and angle in math.<br />
  4. 4. Angles in daily life<br />If we look around us, we will see angles everywhere.<br />
  5. 5. Basic Terms And Definition<br /><ul><li>LINE: A straight path extending in both directions with no endpoints
  6. 6. LINE SEGMENT: A part of a line that includes two </li></ul>points, called endpoints, andall the points between them<br /><ul><li>RAY: A part of a line, with one endpoint, that continues without end in one direction </li></li></ul><li>POINTS<br />An Exact Point Or Location<br />
  7. 7. Intersecting Lines And Non Intersecting Lines<br />Intersecting Lines : Lines that cross<br />Non Intersecting lines : Lines that never cross and are always the same distance apart<br />
  8. 8. Examples Of Non Intersecting Lines<br /><ul><li>Hardwood Floor
  9. 9. Opposite sides of windows, desks, etc.
  10. 10. Parking slots in parking lot
  11. 11. Parallel Parking
  12. 12. Streets: Laramie & LeClaire</li></li></ul><li>Perpendicular lines<br />Two lines that intersect to form four right angles <br />
  13. 13. Examples Of Perpendicular Lines<br /><ul><li>Window Panes
  14. 14. Streets Of Cities</li></li></ul><li>Angles<br />In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other.<br /><ul><li>Acute Angle
  15. 15. Right Angle
  16. 16. Obtuse Angle
  17. 17. Straight angle
  18. 18. Reflex Angle
  19. 19. Adjacent Angles
  20. 20. Linear Pair Of Angles
  21. 21. Vertically Opposite Angles</li></li></ul><li>Acute Angles<br />The measure of an angle with a measure between 0° and 90° or with less than 90° radians.<br />
  22. 22. Examples Of Acute Angles<br />
  23. 23. Right angle<br />An angle formed by the perpendicular intersection of two straight lines; an angle of 90°.<br />
  24. 24. Examples Of Right Angle<br />
  25. 25. Obtuse Angle<br />Angle measures greater than 90 degrees but less than 180 degrees.<br />
  26. 26. Examples Of Obtuse Angle<br />
  27. 27. Straight Angle<br />A straight angle changes the direction to point the opposite way. It looks like a straight line. It measures 180° (half a revolution, or two right angles)<br />
  28. 28. Examples Of Straight Angle<br />
  29. 29. Reflex Angle<br />A Reflex Angle is more than 180° but less than 360°<br />
  30. 30. Adjacent Angles<br />In geometry, adjacent angles, often shortened as adj. ∠s, are angles that have a common ray coming out of the vertex going between two other rays. In other words, they are angles that are side by side, or adjacent.<br />
  31. 31. Linear Pair Of Angles<br />A pair of adjacent angles formed by intersecting lines. Linear pairs of angles are supplementary.<br />
  32. 32. Vertically opposite Angle<br />In geometry, a pair of angles is said to be vertical (also opposite and vertically opposite, which is abbreviated as vert. opp. ∠s) if the angles are formed from two intersecting lines and the angles are not adjacent. They all share a vertex. Such angles are equal in measure and can be described as congruent.<br />
  33. 33. Parallel Lines And Transversal<br />Transversal :- A transversal, or a line that intersects two or more coplanar lines, each at a different point, is a very useful line in geometry.  Transversals tell us a great deal about angles. <br />Parallel Lines :- Parallel lines remain the same distance apart over their entire length. No matter how far you extend them, they will never meet.<br /><ul><li>Corresponding Angles
  34. 34. Alternate Interior Angles
  35. 35. Alternate Exterior Angles
  36. 36. Interior Angles On The Same Side Of the transversal</li></li></ul><li>Corresponding Angles<br />The angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.<br />
  37. 37. Alternate Interior Angle<br />When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and inside the parallel lines, and the angles in each pair are congruent.<br />
  38. 38. Alternate Exterior Angle<br />When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and outside the parallel lines, and the angles in each pair are congruent.<br />
  39. 39. Interior Angles On The Same Side Of the transversal<br />Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles. Further, many a times, we simply use the words alternate angles for alternate interior angles.<br />
  40. 40. The end of This presentation<br />Thank you For Watching It<br />