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4. Example 1-3b Objective Identify special pairs of angles and relationships of angles formed by two parallel lines cut by a transversal

5. Example 1-3b Vocabulary Acute angle An angle that measures of less than 90 0

6. Example 1-3b Vocabulary Right angle An angle that measures 90 0 Right Angle Symbol

7. Example 1-3b Vocabulary Obtuse angle An angle that measures greater than 90 0 but less than 180 0

8. Example 1-3b Vocabulary Straight angle An angle that measures 180 0

9. Example 1-3b Vocabulary Vertical angles Opposite angles formed by the intersection of two lines. Vertical angles are congruent 1 4 2 3  1 =  2 and  3 =  4

10. Example 1-3b Vocabulary Adjacent angles Angles that have the same vertex, share a common side, and do not overlap A B C 1 2  1 and  2 are adjacent angles m  ABC = m  1 + m  2

11. Example 1-3b Vocabulary Complementary angles Two angles are complementary if the sum of their measures is 90 0 B D C A 50 0 40 0  ABC and  DBC are complementary angles m  ABD + m  DBC = 90 0

12. Example 1-3b Vocabulary Supplementary angles Two angles are supplementary if the sum of their measures is 180 0 125 0 55 0 C D  C and  D are supplementary angles m  C + m  D = 180 0

13. Example 1-3b Vocabulary Perpendicular lines Two lines that intersect to form right angles A red right angle symbol indicates that lines m and n are perpendicular m n Symbols: m n

14. Example 1-3b Vocabulary Parallel lines Lines in the same plane that never intersect or cross. The symbol  means parallel p q Red arrowheads indicate that lines p and q are parallel Symbols: p  q

15. Example 1-3b Vocabulary Transversal A line that intersects two or more other lines to form eight angles 1 4 2 3 6 5 7 8

16. Example 1-3b Vocabulary Alternate interior angles Those on opposite sides of the transversal and inside the other two lines are congruent 1 4 2 3 6 5 7 8  2 =  8  3 =  5

17. Example 1-3b Vocabulary Alternate exterior angles Those on opposite sides of the transversal and outside the other two lines are congruent 1 4 2 3 6 5 7 8  4 =  6  1 =  7

18. Example 1-3b Vocabulary Corresponding angles Those in the same position on the two lines in relation to the transversal are congruent 1 4 2 3 6 5 7 8  3 =  7  4 =  8  1 =  5  2 =  6

19. Lesson 1 Contents Example 1Classify Angles and Angle Pairs Example 2Classify Angles and Angle Pairs Example 3Find a Missing Angle Measure ExampleExample 4 Find an Angle MeasureFind an Angle Measure

20. Example 1-1a Classify the angle using all names that apply. acute angle 1/4 There is no right angle symbol m  1 is less than 90 0 Answer:

21. Example 1-1b Classify the angle using all names that apply. Answer: right 1/4

22. Example 1-2a Classify the angle pair using all names that apply.  1 and  2 share the same vertex 2/4  1 and  2 share a common side  1 and  2 do not overlap The above 3 items meets the definition of adjacent angles Adjacent angles;  1 +  2 form a straight line (straight angle) Answer: Straight angle  1 +  2 form a straight line which makes the 2 angles supplementary Supplementary Angles

23. Example 1-2b Classify the angle pair using all names that apply. Answer: adjacent angles, complementary angles 2/4

24. Example 1-3a The two angles below are supplementary. Find the value of x. 3/4 The angles are supplementary which means when added together their measure will equal 180 0 supplementary Write equation Solve equation

25. Example 1-3a The two angles below are supplementary. Find the value of x. 3/4 Ask “what is being done to the variable”? supplementary The variable is being added by 155 Do the inverse on both sides of the equal sign Bring down 155 155 Subtract 155 155 - 155 Bring down + x = 180 155 - 155 + x = 180

26. Example 1-3a The two angles below are supplementary. Find the value of x. 3/4 Subtract 155 supplementary 155 - 155 + x = 180155 - 155 + x = 180 - 155 Combine “like” terms 0 Bring down + x = 0 + x = Combine “like” terms 0 + x = 25 Use Identity Property to add 0 + x x = 25 Add dimensional analysis x = 25 0 Answer:

27. Example 1-3b The two angles below are complementary. Find the value of x. Answer: 35 3/4

28. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 Remember: alternate interior angles are the inside angles of a Z  3 and  2 are interior angles (inside the Z) so they are congruent  2 and  3 are congruent

29. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 Given m  3 = 45 0  2 and  3 are congruent m  2 = 45 0

30. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 m  1 + m  4 + m  2 form a straight line which is 180 0 m  1 + m  4 + m  2 = 180 Given that m  1 = 60 0 60

31. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 m  2 = 45 0 (as solved earlier) m  1 + m  4 + m  2 = 180 Define variable using m  4 60 60 + m  460 + m  4 + 45 = 180 Combine “like” terms m  4 + 105 = 180

32. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 m  1 + m  4 + m  2 = 180 60 60 + m  460 + m  4 + 45 = 180 m  4 + 105 = 180 Ask “what is being done to the variable?” The variable is being added by 105 Do the inverse on both sides of the equal sign Bring down m  4 + 105 m  4 + 105 Subtract 105 m  4 + 105 - 105

33. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 m  1 + m  4 + m  2 = 180 60 60 + m  460 + m  4 + 45 = 180 m  4 + 105 = 180 Bring down = 180 Subtract 105 Combine “like” terms m  4 + 105m  4 + 105 - 105m  4 + 105 - 105 = 180m  4 + 105 - 105 = 180 - 105 m  4 + 0 Bring down = m  4 + 0 = Combine “like” terms m  4 + 0 = 75 Use Identity Property to add m  4 + 0 m  4 = 75 Add dimensional analysis m  4 = 75 0

34. Example 1-4a BRIDGES The sketch below shows a simple bridge design used in the 19th century. The top beam and floor of the bridge are parallel. If and find and 4/4 Remember: you are to find m  2 and m  4 m  2 = 45 0 m  4 = 75 0 Answer:

35. Example 1-3b Answer: BRIDGES The sketch below shows a simple bridge design. The top beam and floor of the bridge are parallel. If and find and * 4/4

36. End of Lesson 1 Assignment Lesson 6:1 Line and Angle Relationships 3 - 26 All