1. Proving Angles Congruent
Geometry 2-5

2. Adjacent angles – Two coplanar angles that share a common side, a common vertex and no interior points
Complementary Angles – Two angles whose measures have a sum of 90
Supplementary Angles – Two angles whose measures have a sum of 180
Angles

3. How to use a protractor
Review

4. Investigation

5. Linear pair – two angles formed from a ray and a line1 2
Definition

6. If two angles form a linear pair, then the measures of the angles add up to 180°2
Conjecture

7. Prove this on a chromebook1 2
Conjecture

8. Geogebra.org

9. Or, maybe…
Geogebra.org

10. Geogebra.org

11. Add an algebra perspective, so we can do some math
Geogebra.org

12. Turn off the axis, so geometry looks much cleaner
Geogebra.org

13. Select the line segment tool
Geogebra.org

14. Add two line segments as shown
Geogebra.org

15. Select the angle measurement tool
Geogebra.org

16. Geogebra.org Measure each angle by clicking on the points
Click in a counterclockwise order
Geogebra.org

17. Geogebra.org Use the move tool to click and move
The angle measurements
Geogebra.org

18. Type this formula in the list on the left
Type this formula in the list on the left. To find the greek letters, use the pop-up keyboard on the bottom

19. Use the move tool to move line segments around, specifically point D
Use the move tool to move line segments around, specifically point D. Watch what happens to the addition of the two angles.

20. Investigation

21. Investigation

22. Vertical Angles – opposite angles formed from intersecting lines1 2
Definition

23. If two angles are vertical angles then they have equal measures1 2
Conjecture

24. Complete this yourself on Geogebra1 2
Conjecture

25. Proofs

26. Proofs can be in different forms

27. We have proven this, we never have to prove it again, and we can use this theorem to help other proofs.
Angles

28. Find the measure of each lettered angle without using a protractor
112°
112°
68°
68°
112°
Examples

29. Find the measure of each lettered angle without using a protractor
20°
70°
20°
110°
70°
Examples

30. Find the measure of each lettered angle without using a protractor
90°
163°
110°
27°
70°
Examples

31. Angles

32. Angles - Practice

33. Angles - Practice

34. Angles - Practice

35. Angles - Practice

36. Angles - Practice

37. Angles - Practice

38. Angles - Practice

39. Angles - Practice

40. Angles - Practice

41. Angles - Practice

42. Angles - Practice

43. Angles - Practice

44. Angles - Practice

45. Angles - Practice

46. Angles - Practice

47. Angles - Practice

48. Pages 100 – 102
1-19, 21, 29, 31, 35, 41, 48, 50
Homework