University:
High School
Course:
High School Geometry
Academic year:

2023
Views:

391

Pages:

5
Author:

Linda Good

Chapter 3 Study Guide Geometry 3.1 Pairs of Lines and Angles Which line(s) or plane(s) appear... parallel to PM: LS, KR, NQ skew to KN: LS, KR, PQ, RS parallel to plane KRL: plane NMQ (back plane) perpendicular to QP: NQ, MP, SP, RQ Classify the angle relationship. Alternate Exterior Alternate Interior Corresponding Consecutive Exterior 3.2 Parallel Lines and Transversals Know what equation to apply for the relationship. Find the value of x and y. Supplementary 50 + x = 180 x = 130 Corresponding 85 = x x = 85 Supplementary y + 85 = 180 y = 95 Vertical 6y + 4 = 128 6y = 124 y = 20.67 Vertical 10x - 15 = 65 10x = 80 x = 8 3.3 Proofs with Parallel Lines Which lines are parallel? (Justify) 120° + 60° = 180° So a||b Corresponding angles are congruent: 47° = 47° Consecutive interior angles: (47°) + (133°) = 180° So x||y Corresponding angles: (135°) + (4x - 3) = 180° 4x = 48 x = 12 So a||b Corresponding angles: (8x) + (2x) = 180° 10x = 180 x = 18 So x is not parallel to y 3.4 Proofs with Perpendicular Lines Determine which lines, if any, must be parallel. Explain your reasoning. a ⊥ x b ⊥ x So a||b (using the Perpendicular Line Rule) a ⊥ y b ⊥ y So a||b (using the Parallel Line Rule) a ⊥ x b ⊥ y We can't use this to claim anything parallel a ⊥ y b ⊥ x So, using the Perpendicular Line Rule, a||b 3.5 Equations of Parallel and Perpendicular Lines Are the lines parallel, perpendicular, or neither? (Justify) 1. Line A: (1, 2), B(3, -2) Line B: (2, 0), B(-3, -2) Slope(line 1) = (-2 - 2) / (3 - 1) = -4/2 = -2 Slope(line 2) = (-2 - 0) / (-3 - 2) = -2/-5 = 2/5 Since the slopes are the same, these lines are parallel. 2. [A diagram of two lines intersecting on a coordinate grid is shown.] Slope = -9/3 = -3 Slope = 7/2 These slopes are neither the same nor (-1) reciprocals, so these lines are neither.