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Warm up: In the figure, a b, and c is the transversal. a c 1 3 4 2 b 5 7 8 6 1. Which angle is a corresponding angle with 5? 2. Which angles are congruent to 2 and 3? 3. Find the measure of 8 if m 3 = 78. 4. Find the measure of 6 if m 2 = 84. 5. Find x if m 1 = 9x and m 5 = 6(x + 5). 1 Review for Quiz 41 & 42 1. Describe each pair of segments as parallel, skew or intersecting. X a. BD and XZ b. FY and ZY c. BF and YZ Y B F Z D 2. Find the measures of the angles. a. Find m 16, if m 10 = 75 b. Find m 1, if m 13 = 83 6 5 7 8 c. Find m 8, if m 9 = 45 2 1 3 4 d. Find m 4, if m 14 = 133 10 9 11 12 14 13 15 16 2 3. Find the values of x and y. (4y + 2)° 4x° (x + 5)° (2y + 8)° OBJECTIVE: You will learn to identify conditions that produce parallel lines and to construct parallel lines. Section 44 ______________ Postulate 42 In a plane, if two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are parallel. 1 a 2 b If 1 = 2, then a b. 3 Example 1: If m 1 = 13x 8 and m 2 = 12x + 4, find x so that l m. l 2 3 1 m Theorem 45 In a plane, if two lines are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel. Theorem 46 In a plane, if two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel. Theorem 47 In a plane, if two lines are cut by a transversal so that a pair of sameside interior angles is supplementary, then the two lines are parallel. 4 Theorem 48 In a plane, if two lines are perpendicular to the same line, then the two lines are parallel. 5 ways to prove two lines are parallel • show corresponding angles are congruent • show alternate interior angles are congruent • show alternate exterior angles are congruent • show sameside interior angles are supplementary • show that two lines in a plane are perpendicular to a third line Example 2: Identify the parallel segments in the letter z. A 40° C B 40° D Example 3: Find the value of x so BE TS. B E (4x + 8)° (2x + 10)° (5x + 2)° T S 5 Hands on Geometry p. 162 1. Use a straightedge to draw a line l and a point P not on l. 2. Draw a line t through P that intersects line l. Label the angle between the lines as 1. 3. Use a compass and a straightedge to construct an angle congruent to 1 at P. Label this angle 2. 4. Extend the side of 2 to form line m (which is parallel to line l ). QUESTIONS: 1. What relationship do angles 1 and 2 have? 2. Use a ruler to measure the distance between lines l and m at several places. Make a conjecture about the relationship between the lines. Guided Practice: Find x so that a b. a b 1. 2. 84° a 10x° 5x° 3x° b 6 Name the pairs of parallel lines or segments. S 3. 4. p 113° Q U 42° 42° q 67° 68° 42° r R T s Do you have any Vocab questions? OBJECTIVE: HOMEWORK: p. 166 167 # 9 20, 25 29 7