1. Lines, Angles, and Triangles, Oh My! Kristian Wilks – Lake Shore Justin Lumpkins – Warren Mott

2. Wilks and Lumpkins2 GLCE G.GS.06.01 Grade Level Content Expectations Introduction to Geometry http://www.tutorvista.com/math/different-triangles-tutor

3. Wilks and Lumpkins3 Purpose Explore different types of: –Angles –Triangles Show relations of: –Vertical Angles –Complementary Angles –Supplementary Angles

4. Wilks and Lumpkins4 Purpose Continued When parallel lines cut by a transversal, explore congruence of: –Corresponding Angles –Alternate Interior Angles Implications of parallel lines

5. Wilks and Lumpkins5 Lines Line: A continuous extent of length

6. Angles Wilks and Lumpkins6

7. 7 Definition Angle: The space within two lines diverging from a common point

8. Types Of Angles Wilks and Lumpkins8

9. Acute Angles Measure = Less than 90° Wilks and Lumpkins9

10. Right Angles Measure = Exactly 90° Wilks and Lumpkins10

11. Obtuse Angles Measure = More than 90° Wilks and Lumpkins11

12. Angle Relationships Wilks and Lumpkins12

13. Adjacent Angles Two angles side by side Angle measure does not matter Wilks and Lumpkins13 A B Angle A and B are adjacent to each other.

14. Complementary Angles Two acute angles side by side Combined angle measure = 90° Wilks and Lumpkins14

15. Supplementary Angles Two angles side by side –Right and Right –Obtuse and Acute Combined angle measure = 180° Wilks and Lumpkins15

16. Vertical Angles 4 angles formed by intersecting lines, add up to = 360° Opposite angles are congruent Wilks and Lumpkins16 2 1 3 4 m<1 = m<3 M<2 = m<4

17. Parallel Lines & Angles Cut by transversal Wilks and Lumpkins17 Transversal Alt. Int. Angles C and G D and F Corresponding Angles H and C F and A E and D G and B

18. Triangles Wilks and Lumpkins18

19. Definition Triangle: 3 sided polygon whose angles add up to 180° Wilks and Lumpkins19

20. Types Of Triangles Wilks and Lumpkins20

21. Acute Triangles Angles: 3 Acute Wilks and Lumpkins21

22. Right Triangles Angles: 1 Right, 2 Acute Wilks and Lumpkins22

23. Obtuse Triangles Angles: 1 Obtuse, 2 Acute Wilks and Lumpkins23

24. Scalene Triangles 3 different angle measures Wilks and Lumpkins24

25. Isosceles Triangles 2 congruent angles Wilks and Lumpkins25

26. Equilateral Triangles All 3 angles are congruent Wilks and Lumpkins26

27. Recap 6 different types of basic angles and triangles Vertical angles are always congruent Two lines cut by a transversal and have congruent corresponding and alternate interior angles are parallel Wilks and Lumpkins27

28. Resources Wilks and Lumpkins28 http://www.ies.co.jp/math/products/geo1/applets/ kakuhei/kakuhei.html http://www.mathsisfun.com/geometry/parallel- lines.html http://www.michigan.gov/documents/mde/CADD _Math_Wayne_Westland_226351_7.doc Geometry and Algebra with Transformations Course Packet

29. Any Questions? Wilks and Lumpkins29

30. Wilks and Lumpkins30 JK Jeopardy

31. Wilks and Lumpkins31 Angles Measurements Triangles and Angles Triangle TypesAngle TypesMiscellaneous 1 2 3 1111 2 2 22 3333

32. Wilks and Lumpkins32 What is the angle measure of a right angle?

33. Wilks and Lumpkins33 What is the combined angle measured of complementary angles?

34. Wilks and Lumpkins34 What is the combined angle measure of supplementary angles?

35. Wilks and Lumpkins35 Which triangle has three congruent angles?

36. Wilks and Lumpkins36 Which triangle has one right angle and two acute angles?

37. Wilks and Lumpkins37 Which triangle has no congruent angles?

38. Wilks and Lumpkins38 Which angle measure more than 90°?

39. Wilks and Lumpkins39 Which angles add up to 360°?

40. Wilks and Lumpkins40 Which angle is larger than an acute angle but smaller than an obtuse angle?

41. Wilks and Lumpkins41 What angles and how many of each make an obtuse triangle?

42. Wilks and Lumpkins42 How many angles are congruent on an isosceles triangle?

43. Wilks and Lumpkins43 How many right angles are in a right triangle?

44. Wilks and Lumpkins44 What is a transversal?

45. Wilks and Lumpkins45 What is the definition of a line?

46. Wilks and Lumpkins46 What is the definition of an angle?