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Plane Geometry

Plane Geometry. Points, Lines, Planes & Angles. Vocabulary Point – Names a location Line – Perfectly straight and extends in both directions forever Plane - Perfectly flat surface that extends forever in all directions Segment – Part of a line between two points

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Plane Geometry

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  1. Plane Geometry

  2. Points, Lines, Planes & Angles Vocabulary • Point – Names a location • Line – Perfectly straight and extends in both directions forever • Plane - Perfectly flat surface that extends forever in all directions • Segment – Part of a line between two points • Ray – Part of a line that starts at a point and extends forever in one direction

  3. Point

  4. Line

  5. Segment

  6. Ray

  7. Example 1 • Name four points • Name the line • Name the plane • Name four segments • Name five rays

  8. More Vocabulary • Right Angle – Measures exactly 90° • Acute Angle – Measures less than 90 ° • Obtuse Angle – Measures more than 90 ° • Complementary Angle – Angles that measure 90 ° together • Supplementary Angle – Angles that measure 180 ° together

  9. Right Angle

  10. Acute Angle

  11. Obtuse Angle

  12. Complementary Angle

  13. Supplementary Angle

  14. Example 2 • Name the following: • Right Angle • Acute Angle • Obtuse Angle • Complementary Angle • Supplementary Angle

  15. Even MORE Vocabulary • Congruent – Figures that have the same size AND shape • Vertical Angles • Angles A & C are VA • Angles B & D are VA • If Angle A is 60° what is the measure of angle B?

  16. Parallel and Perpendicular Lines Vocabulary • Parallel Lines – Two lines in a plane that never meet, ex. Railroad Tracks • Perpendicular Lines – Lines that intersect to form Right Angles • Transversal – A line that intersects two or more lines at an angle other than a Right Angle

  17. Parallel Lines

  18. Perpendicular Lines

  19. Transversal

  20. Transversals to parallel lines have interesting properties • The color coded numbers are congruent

  21. Properties of Transversals to Parallel Lines • If two parallel lines are intersected by a transversal: • The acute angles formed are all congruent • The obtuse angles are all congruent • And any acute angle is supplementary to any obtuse angle • If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles

  22. Alternate Interior Angles

  23. Alternate Exterior Angles

  24. Corresponding Angles

  25. Symbols • Parallel • Perpendicular • Congruent

  26. Example 1 • In the figure Line X Y • Find each angle measure

  27. In the figure Line A B • Find each angle measure

  28. Triangle Sum Theorem – The angle measures of a triangle in a plane add to 180° Because of alternate interior angles, the following is true: Triangles

  29. Vocabulary • Acute Triangle – All angles are less than 90° • Right Triangle – Has one 90° angle • Obtuse Triangle – Has one obtuse angle

  30. Example • Find the missing angle

  31. Example • Find the missing angle.

  32. Example • Find the missing angles

  33. Vocabulary • Equilateral Triangle – 3 congruent sides and angles • Isosceles Triangle – 2 congruent sides and angles • Scalene Triangle – No congruent sides or angles

  34. Equilateral Triangle • Isosceles Triangle • Scalene Triangle

  35. Remember…they are ALL triangles

  36. Example • Find the missing angle(s)

  37. Example • Find the missing angle(s)

  38. Example • Find the missing angle(s)

  39. Example • Find the angles. Hint, remember the triangle sum theorem

  40. Polygons • Polygons • Have 3 or more sides • Named by the number of sides • “Regular Polygon” means that all the sides are equal length

  41. Finding the sum of angles in a polygon • Step 1: • Divide the polygon into triangles with common vertex

  42. Step 2: • Multiply the number of triangles by 180

  43. The Short Cut • 180°(n – 2) where n = the number of angles in the figure • In this case n = 6 • = 180°(6 – 2) • = 180°(4) • = 720° *Notice that n - 2 = 4 **Also notice that the figure can be broken into 4 triangles…coincidence? I don’t think so!

  44. Example • Find the missing angle

  45. This chart may help…

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