Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3-3 Lines Parallel 3-5 Proving Showing Lines are Parallel Warm Up Lesson Presentation Lesson Quiz Holt Geometry Holt Geometry 3-5 Proving Lines Parallel 3-3 Objective Use the angles formed by a transversal to prove two lines are parallel. Holt Geometry 3-5 Proving Lines Parallel 3-3 If two parallel lines are cut by a transversal, then the corresponding angles are congruent. 100 100 Corresponding Angles Converse: If 2 lines are cut by a transversal so the corresponding angles are congruent _______________, then the lines parallel are ______________. Holt Geometry 3-5 Proving Lines Parallel 3-3 If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. 50 50 Alt. Interior Angles Converse: If 2 lines are cut by a transversal so the alternate interior angles are congruent ______________, then the parallel lines are _____________. Holt Geometry 3-5 Proving Lines Parallel 3-3 If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. 60 60 Alt. Exterior Angles Converse: If 2 lines are cut by a transversal so the alternate exterior angles are congruent _____________, then the parallel lines are ____________. Holt Geometry 3-5 Proving Lines Parallel 3-3 If two parallel lines are cut by a transversal, then the consecutive interior angles are supplementary. 80 100 Consecutive Angles Converse: If 2 lines are cut by a transversal so the consecutive interior angles supplementary then the are _______________, parallel lines are ___________. Holt Geometry 3-5 Proving Lines Parallel 3-3 Example 1: Using the Converse of Angle Relationships A) Use the given information to identify the relationship that could be used to show that ℓ || m. 4 8 Yes, ℓ || m because of the Converse of Corresponding Holt Geometry 3-5 Proving Lines Parallel 3-3 B) Use the given information to identify the relationship that could be used to show that ℓ || m. (aka plug in the value of x and see if it gives you a true statement.) m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30 m3 = 4(30) – 80 = 40 m7 = 3(30) – 50 = 40 3 7 Yes, ℓ || m because of the Converse of Corresponding Holt Geometry 3-5 Proving Lines Parallel 3-3 C) Use the given information to identify the relationship that could be used to show that ℓ || m. m7 = (4x + 26)°, m2 = (5x + 12)°, x = 13 m7 = 4(13) + 26 = 78 m2 = 5(13) + 12 = 77 Substitute 13 for x. Substitute 13 for x. m7 = m2 ℓ is not parallel to m because alternate interior angles should be congruent, and these two angles are not. Holt Geometry 3-5 Proving Lines Parallel 3-3 D) Use the given information to identify the relationship that could be used to show that ℓ || m. m1 = (3x + 10)°, m8 = (4x - 10)°, x = 20 m1 = 3(20) + 10 = 70 Substitute 13 for x. m8 = 4(20) - 10 = 70Substitute 13 for x. m1 = m8 Yes, ℓ || m because of the converse of alternate exterior angles Holt Geometry 3-5 Proving Lines Parallel 3-3 E) Use the given information to identify the relationship that could be used to show that r || s. m2 = (10x + 8)°, m3 = (25x – 67)°, x = 5 m2 = 10x + 8 = 10(5) + 8 = 58 m3 = 25x – 67 = 25(5) – 67 = 58 m2 + m3 = 58° + 58° = 116° 2 and 3 are same-side interior angles. So, r is not parallel to s because the angles should =180 Holt Geometry