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Transparency 1. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 1-3b. Objective. Identify special pairs of angles and relationships of angles formed by two parallel lines cut by a transversal. Example 1-3b. Vocabulary. Acute angle.

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  1. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

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

  4. Example 1-3b Vocabulary Acute angle An angle that measures of less than 900

  5. Example 1-3b Vocabulary Right angle An angle that measures 900 Right Angle Symbol

  6. Example 1-3b Vocabulary Obtuse angle An angle that measures greater than 900 but less than 1800

  7. Example 1-3b Vocabulary Straight angle An angle that measures 1800

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

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

  10. Example 1-3b Vocabulary Complementary angles Two angles are complementary if the sum of their measures is 900 A D 500 400 B C ABC and DBC are complementary angles m ABD + m DBC = 900

  11. Example 1-3b Vocabulary Supplementary angles Two angles are supplementary if the sum of their measures is 1800 C 1250 550 D C and D are supplementary angles m C + m D = 1800

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

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

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

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

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

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

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

  19. Example 1-1a Classify the angle using all names that apply. There is no right angle symbol m1 is less than 900 Answer: acute angle 1/4

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

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

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

  23. Example 1-3a The two angles below are supplementary. Find the value of x. supplementary The angles are supplementary which means when added together their measure will equal 1800 Write equation Solve equation 3/4

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

  25. Example 1-3a The two angles below are supplementary. Find the value of x. supplementary Subtract 155 Combine “like” terms Bring down + x = Combine “like” terms Use Identity Property to add 0 + x 155 - 155 + x = 180 - 155 155 - 155 + x = 180 Add dimensional analysis 0 + x = 25 0 0 + x = x = 25 Answer: x = 250 3/4

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

  27. BRIDGESThe 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 Example 1-4a 2 and 3 are congruent Remember: alternate interior angles are the inside angles of a Z 3 and 2 are interior angles (inside the Z) so they are congruent 4/4

  28. BRIDGESThe 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 Example 1-4a 2 and 3 are congruent m 2 = 450 Given m 3 = 450 4/4

  29. BRIDGESThe 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 Example 1-4a m1 + m 4 + m 2 = 180 60 m 1 + m 4 + m 2 form a straight line which is 1800 Given that m 1 = 600 4/4

  30. BRIDGESThe 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 Example 1-4a m1 + m 4 + m 2 = 180 60 60 + m 4 60 + m 4 + 45 = 180 m 4 + 105 = 180 Define variable using m 4 m 2 = 450 (as solved earlier) Combine “like” terms 4/4

  31. BRIDGESThe 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 Example 1-4a Ask “what is being done to the variable?” m1 + m 4 + m 2 = 180 60 60 + m 4 60 + m 4 + 45 = 180 The variable is being added by 105 m 4 + 105 = 180 Do the inverse on both sides of the equal sign m 4 + 105 m 4 + 105 - 105 Bring down m 4 + 105 Subtract 105 4/4

  32. BRIDGESThe 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 Example 1-4a Bring down = 180 m1 + m 4 + m 2 = 180 Subtract 105 60 60 + m 4 60 + m 4 + 45 = 180 Combine “like” terms m 4 + 105 = 180 Bring down = m 4 + 105 - 105 m 4 + 105 m 4 + 105 - 105 = 180 - 105 m 4 + 105 - 105 = 180 Combine “like” terms m 4 + 0 m 4 + 0 = m 4 + 0 = 75 Use Identity Property to add m 4 + 0 m 4 = 75 m 4 = 750 Add dimensional analysis 4/4

  33. BRIDGESThe 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 Example 1-4a Answer: m 2 = 450 m 4 = 750 Remember: you are to find m 2 and m 4 4/4

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

  35. End of Lesson 1 Assignment

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