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Plane Geometry

Explore various concepts in plane geometry, including points, lines, planes, segments, rays, angles, and polygons. Learn about properties of angles, parallel and perpendicular lines, triangles, and polygons, with helpful examples and vocabulary.

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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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