1. 10/15/20151.7: Angle Relationships 1-7: Angle Relationships Expectations: 1.You will be able to solve problems involving congruent and supplementary angles. 2.You will be able to explain the difference between adjacent angles and linear pairs of angles. 3.You will be able to use the linear pair postulate and the vertical angle theorem to solve problems.

2. Do you remember … 1.Complementary angles 2.Supplementary angles 3.Perpendicular lines 10/15/20151.7: Angle Relationships

3. 10/15/20151.7: Angle Relationships Complementary Angles Defn: Two angles are complementary iff the sum of their measures is ____. 90

4. 10/15/20151.7: Angle Relationships Angle A is complementary to angle B. If m ∠ B is 3 less than twice m ∠ A, what are m ∠ A and m ∠ B?

5. 10/15/20151.7: Angle Relationships Supplementary Angles Defn: Two angles are supplementary iff the sum of their measures is ________.

6. 10/15/20151.7: Angle Relationships Perpendicular Lines Defn: Two lines l and m are perpendicular, written l ⊥ m, iff they intersect to form ________________________. l m

7. Now some new terms. 10/15/20151.7: Angle Relationships

8. 10/15/20151.7: Angle Relationships Adjacent Angles Defn: Two angles are adjacent iff they share a ___________________, but have no interior points in common.

9. 10/15/20151.7: Angle Relationships 1 2 Angles 1 and 2 are adjacent angles.

10. 10/15/20151.7: Angle Relationships 1 2 3 4 Angles 1 and 3 (and 2 and 4) are not adjacent angles. Why?

11. 10/15/20151.7: Angle Relationships A B C D ∠ ABC and ∠ ABD are not adjacent. Why?

12. In the figure below, which pairs of angles are adjacent angles? A. ∠ 2 and ∠ 3 B. ∠ 7 and ∠ 8 C. ∠ 4 and ∠ 5 D. ∠ 2 and ∠ 7 E. ∠ 4 and ∠ 6 10/15/20151.7: Angle Relationships 1 2 3 4 57 86

13. 10/15/20151.7: Angle Relationships Linear Pair Defn: Two adjacent angles form a linear pair iff their non-common sides are _________________.

14. 10/15/20151.7: Angle Relationships 12 ∠ 1 and ∠ 2 form a linear pair.

15. Draw a pair of adjacent angles that do not form a linear pair. 10/15/20151.7: Angle Relationships

16. Geometers Sketch Pad “Linear Pairs.” 10/15/20151.7: Angle Relationships

17. 10/15/20151.7: Angle Relationships Linear Pair Postulate If two angles form a linear pair, then they are __________________.

18. 10/15/20151.7: Angle Relationships Vertical Angles Defn: Two angles are vertical angles iff they are ______________ angles formed by two intersecting lines. 1 4 3 2

19. Quick “Quiz” 10/15/20151.7: Angle Relationships

20. 10/15/20151.7: Angle Relationships What type of angles are these? 1 2

21. 10/15/20151.7: Angle Relationships What type of angles are these? 1 2

22. 10/15/20151.7: Angle Relationships What type of angles are these? 1 2

23. 10/15/20151.7: Angle Relationships Vertical Angles and Linear Pairs Geometers Sketch Pad “Vertical Angles.”

24. 10/15/20151.7: Angle Relationships Vertical Angle Theorem If two angles are vertical angles, then they are ____________.

25. 10/15/20151.7: Angle Relationships Determine whether the following are true or false: a. If 2 angles are supplementary, then they form a linear pair. b. If 2 angles form a linear pair, then they are supplementary.

26. 10/15/20151.7: Angle Relationships What are the measures of all of the angles below? 1 3 2 4

27. 10/15/20151.7: Angle Relationships Perpendicular Lines Theorem Two Perpendicular lines form ___ right angles.

28. 7 minute write Using geometrical terms and complete sentences, tell me (in writing) why you know the Perpendicular Lines Theorem must be true. This will be handed in and corrected for points. 10/15/20151.7: Angle Relationships

31. 10/15/20151-7: Angle Relationships 31 Determine the measure of each angle if m ∠ 1=5x+11 and m ∠ 2=8x-1. 12 34 A.31, 31 B.31, 59 C.31, 149 D.41.95, 48.25 E.76.4, 103.6

32. What is the difference of the measures of angles 1 and 2 in the diagram below if m ∠ 1 = 8x + 4 and m ∠ 2 = 12x – 8, rounded to the nearest whole number? A.0 B.3 C.6 D.9 E.25 10/15/20151-7: Angle Relationships 32 ∠1∠1 ∠2∠2

33. 10/15/20151.7: Angle Relationships Things you may assume from an unmarked drawing collinear points, betweenness, intersections, position of figures with relationship to one another, opposite rays, adjacent angles, linear pairs These are really important!!!!

34. 10/15/20151.7: Angle Relationships Things you should not assume from a drawing measures, perpendicular lines, parallel lines, congruence, midpoints, bisectors, supplementary angles, complementary angles. These are even more important!!!!!

35. 10/15/20151.7: Angle Relationships Assignment pages 59, # 15 – 25 (odds), 29 and 31 and pages 111 – 112, # 22 – 32 (evens)