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G E O M E T R Y

G E O M E T R Y. Math 7 Unit 4. Standards. GEOMETRY IS EVERYWHERE. IN FLAGS. IN NATURE. IN SPORTS. IN MUSIC. IN SCIENCE. IN Games. IN BUILDINGS. The hardest part about Geometry. Vocabulary. A. Point. : a location in space. : think about the tip of your pencil. Notation :. ●A.

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G E O M E T R Y

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  1. GEOMETRY Math 7 Unit 4

  2. Standards

  3. GEOMETRY IS EVERYWHERE

  4. IN FLAGS

  5. IN NATURE

  6. IN SPORTS

  7. IN MUSIC

  8. IN SCIENCE

  9. IN Games

  10. IN BUILDINGS

  11. The hardest part about Geometry Vocabulary

  12. A Point : a location in space : think about the tip of your pencil Notation : ●A

  13. A B Line all the points on a never-ending straight path that extends in all directions Notation :

  14. C D Segment all the points on a straight path between 2 points, including those endpoints Notation :

  15. E F Ray a part of a line that starts at a point (endpoint) and extends forever in one direction Notation :

  16. Side A 1 B C Side Vertex Angle formed by 2 rays that share the same endpoint. The point is called the VERTEX and the rays are called the sides. Angles are measure in degrees. 70

  17. A 15° B C Angle Notation :

  18. A Plane a flat surface without thickness extending in all directions Think: a wall, a floor, a sheet of paper Notation :

  19. C A B D Parallel Lines lines that never intersect (meet) and are the same distance apart Notation : ║

  20. D A B C Perpendicular Lines lines that meet to form right angles Notation :

  21. D A B C Intersecting Lines lines that meet at a point

  22. Right Angle An angle that measures 90 degrees.

  23. Straight Angle An angle that measures 180 degrees or 0. (straight line)

  24. Acute Angle An angle that measures between 1 and 89 degrees

  25. Obtuse Angle An angle that measures between 91 and 179 degrees

  26. 2 1 Complementary Angles Two or more angles whose measures total 90 degrees.

  27. 2 1 Supplementary Angles Two or more angles that add up to 180 degrees.

  28. *****Reminders****** Supplementary Straight angle Complimentary Corner

  29. A D B C Adjacent Angles Two angles who share a common side

  30. Example 1 • Estimate the measure of the angle, then use a protractor to find the measure of the angle.

  31. 2 60 1 Example 1 • Angles 1 and 2 are complementary. If • m 1 = 60, find m 2. 1 + 2 = 90 2 = 90 - 1 2 = 90 - 60 2 = 30

  32. 114 1 2 Example 3 • Angles 1 and 2 are supplementary. If m 1 is 114, find m 2. < 1 + < 2 = 180 < 2 = 180 - < 1 < 2 = 180 - 114 < 2 = 66

  33. 7.2 Angle Relationships t 1 2 4 3 6 5 7 8

  34. Vertical Angles • Two angles that are opposite angles. • Vertical angels are always congruent! • 13 • 2  4

  35. t 125  ? ? Vertical Angles • Example 1: Find the measures of the missing angles 125  55 

  36. B A D l C m AB || CD l || m PARALLEL LINES • Def: line that do not intersect. • Illustration:

  37. Examples of Parallel Lines • Hardwood Floor • Opposite sides of windows, desks, etc. • Parking slots in parking lot • Parallel Parking • Streets: Arizona Avenue and Alma School Rd.

  38. Examples of Parallel Lines • Streets: Belmont & School

  39. Transversal • Def: a line that intersects two lines at different points • Illustration: t

  40. t 1 2 4 3 6 5 7 8 Supplementary Angles/Linear Pair • Two angles that form a line (sum=180) • 1+2=180 • 2+4=180 • 4+3=180 • 3+1=180 • 5+6=180 • 6+8=180 • 8+7=180 • 7+5=180

  41. Supplementary Angles/Linear Pair • Find the measures of the missing angles t ? 108  72  ? 108 

  42. Alternate Exterior Angles • Two angles that lie outside parallel lines on opposite sides of the transversal t • 2  7 • 1  8 1 2 3 4 5 6 7 8

  43. Alternate Interior Angles • Two angles that lie between parallel lines on opposite sides of the transversal t • 3  6 • 4  5 1 2 3 4 5 6 7 8

  44. 1 2 3 4 5 6 7 8 Corresponding Angles • Two angles that occupy corresponding positions. t • 15 • 2  6 • 3  7 • 4  8 Top Left Top Right Bottom Left Bottom Right Top Left Top Right Bottom Left Bottom Right

  45. Same Side Interior Angles 3 +5 = 180 • 4 +6 = 180 • Two angles that lie between parallel lines on the same sides of the transversal t 1 2 3 4 5 6 7 8

  46. 5 6 4 7 8 3 2 t 1 List all pairs of angles that fit the description. • Corresponding • Alternate Interior • Alternate Exterior • Consecutive Interior

  47. Find all angle measures t 180 - 67 113  67  1 3 67  2 113  113  5 67  8 67  6 7 113 

  48. Example 5: • find the m 1, if m 3 = 57 • find m 4, if m 5 = 136 • find the m 2, if m 7 = 84

  49. 36  x  Algebraic Angles = 90 • Name the angle relationship • Are they congruent, complementary or supplementary? • Complementary • Find the value of x x + 36 = 90 -36 -36 x = 54

  50. 115  x  Example 2 • Name the angle relationship • Vertical • Are they congruent, complementary or supplementary? • Find the value of x  x = 115 

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