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Lesson 3-1

Lesson 3-1. Parallel Lines and Transversals. Transparency 3-1. 5-Minute Check on Chapter 2. 1. Make a conjecture about the next item in the sequence: 5, 20, 80, 320. 2. Write the contrapositive for this statement: If you live in Boston, then you live in Massachusetts.

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Lesson 3-1

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  1. Lesson 3-1 Parallel Lines and Transversals

  2. Transparency 3-1 5-Minute Check on Chapter 2 1. Make a conjecture about the next item in the sequence: 5, 20, 80, 320. 2. Write the contrapositive for this statement: If you live in Boston, then you live in Massachusetts. 3. Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements: If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles. 4. Name the property that justifies the statement. If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75. 5. Find m1 and m2 if m1 = 8x + 18, and m2 = 16x – 6. 6. The measures of two complementary angles are in the ratio 7:8. What is the measure of the larger angle? Standardized Test Practice: 96 A 42 B C 84 D 48

  3. Transparency 3-1 5-Minute Check on Chapter 2 1. Make a conjecture about the next item in the sequence: 5, 20, 80, 320. 1280 2. Write the contrapositive for this statement: If you live in Boston, then you live in Massachusetts. If you do not live in Massachusetts, then you do not live in Boston. 3. Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements: If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles. no conclusion 4. Name the property that justifies the statement. If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75. Substitution Property 5. Find m1 and m2 if m1 = 8x + 18, and m2 = 16x – 6. m1 = 74; m2 = 106 6. The measures of two complementary angles are in the ratio 7:8. What is the measure of the larger angle? Standardized Test Practice: 96 A 42 B C 84 D 48

  4. Objectives • Identify the relationships between two lines or two planes • Name angles formed by a pair of lines and a transversal

  5. Vocabulary • Parallel symbol (||) • Parallel lines – coplanar lines that do not intersect • Parallel planes – planes that do not intersect • Skew lines – lines that do not intersect and are not coplanar • Transversal – a line that intersects two or more coplanar lines at different points

  6. t k 1 2 3 4 5 6 l 7 8 Angles formed by Transversals

  7. t k 1 2 3 4 5 6 l 7 8 Solving Angle Problems • 95% of all angle problems are solved by one of two equations: • Angle = Angle (angles are congruent) • Angle + Angle = 180 (angles are supplementary) Angle = Angle m1 = m4 3x + 10 = 4x – 30 +30 = +30 3x + 40 = 4x -3x = -3x 40 = x Angle + Angle = 180 m1 + m2 = 180 4x – 30 + x + 10 = 180 5x – 20 = 180 +20 = +20 5x = 200 x = 40

  8. Name all segments that intersect Answer: Given the following figure: Name all planes that are parallel to plane AEF. Answer: plane BHG

  9. Name all segments that are parallel to Name all segments that are skew to Answer: Answer: Given the following figure:

  10. a. Name all planes that are parallel to plane RST. b. Answer: c. Answer: d. Answer: Use the figure to name each of the following. Answer: plane XYZ

  11. BUS STATION Some of a bus station’s driveways are shown as lines u, v, w, x, y and z. Identify the sets of lines to which line vis a transversal. Answer: If the lines are extended, line v intersects lines u, w, x, and z. Identify the sets of lines to which line yis a transversal. Answer: lines u, w, x, z

  12. BUS STATION Some of a bus station’s driveways are shown as lines u, v, w, x, y and z. Identify the sets of lines to which line uis a transversal. Answer: lines v, x, y, z Identify the sets of lines to which line wis a transversal. Answer: lines v, x, y, z

  13. a. line a b. line b c. line c d. line d HIKING A group of nature trails is shown. Identify the sets of lines to which each given line is a transversal. Answer: lines c, d, e, f Answer: lines c, d, e, f Answer: lines a, b, d, e, f Answer: lines a, b, c, e, f

  14. Given the following figure, identify each set of angles as alternate interior, alternate exterior, corresponding, or consecutive interiorangles. Answer: corresponding Answer: alternate exterior Answer: consecutive interior Answer: alternate interior

  15. d. a. b. e. c. f. Identify each set of angles as alternate interior, alternate exterior, corresponding, or consecutive interiorangles. Answer: consecutive interior Answer: corresponding Answer: alternate exterior Answer: alternate interior Answer: corresponding Answer: alternate exterior

  16. Summary & Homework • Summary: • Coplanar lines that do not intersect are called parallel • When two lines are cut by a transversal, there are many angle relationships • Homework: • pg 129 – 131: 11-17, 70-75

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