Notes Formal Geometry Chapter 3 Parallel and Perpendicular Lines
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1 Name Date Period Notes Formal Geometry Chapter 3 Parallel and Perpendicular Lines 3-1 Parallel Lines and Transversals and 3-2 Angles and Parallel Lines A. Definitions: 1. Parallel Lines: Coplanar lines that do NOT intersect 2. Skew Lines: Lines that do NOT intersect and are NOT coplanar 3. Parallel Planes: Planes that do NOT intersect 4. Transversal: Line that intersects two or more coplanar lines at two different points 5. Interior Angles: Region that lies between two lines 6. Exterior Angles: Region that lies outside two lines 7. Consecutive Interior Angles: Interior angles that lie on the same side of a transversal 8. Alternate Interior Angles: Nonadjacent interior angles that lie on opposite sides of a transversal 9. Alternate Exterior Angles: Nonadjacent exterior angles that lie on opposite sides of a transversal 10. Corresponding Angles: Lie on the same side of a transversal and on the same side of the intersecting lines B. Examples: 1. 1
2 2. C. Guided Practice: D. Definitions: 1. Corresponding Angles Postulate: 2. Sd 3. Sd 4. 2
3 5. Perpendicular Transversal Theorem: E. Examples:
4 Geometry Constructions #2 - Perpendicular Lines, Line Parallel to a Given Line This website is a great resource for constructions: 1. Constructing a Line Perpendicular to a Point on a Given Line 4
5 2. Constructing a Line Parallel to a Given Line Through a Point not on Given Line 5
6 3.3 Slopes of Lines A. Opener: Use the figure at the right to determine the relationship between each pair of angles. 1. <1 and <7 2. <5 and <3 3. <2 and <6 B. Definitions: 1. Slope/Rate of Change: 2. Slope of Parallel Lines: 3. Slope of Perpendicular Lines: C. Examples:
7 4. Must show all work!
8 D. Guided Practice: t 3. t 4. gh 3.4 Equations of Lines A. Opener: B. Definitions: 1. Slope Intercept Form: 2. Point Slope Form: 3. Horizontal Line Equation: 8
9 4. Vertical Line Equation: C. Examples: 1. Write an equation in slope-intercept form of the line with slope 5 and y-intercept of -7. Then graph the line. 2. Write an equation in point-slope form of an equation with a slope of 1 that contains (-2, 5). Then 4 graph the line. 3. Write an equation of the line through (0, 3) and (-2, -1) in slope intercept form. 4. Write an equation of the line through (-2, 4) and (10, 4) in slope intercept form. 5. Write an equation in slope intercept form for a line perpendicular to the line y=-3x+2 through (4,0). 9
10 D. Guided Practice: 1. Write an equation in slope-intercept form of the line with slope -1 and y-intercept of -2. Then graph the line. 2. Write an equation in point-slope form of an equation with a slope of 1/3 that contains (-1, 5). Then graph the line. 3. Write an equation of the line through (-7, 4) and (9, -4) in slope intercept form. 4. Write an equation of a line in slope intercept form of a line that is parallel to and passes through (9, -1). 10
11 3.4 Continued - Solving Systems of Equations A. Examples: Use elimination to solve each system of equations. 1. 4x 3y = x 2 y 4 4x 2y 10 2x + 3y = x + 5y = x 6y = -12 -x + 3y = -7 x + 2y = 0 5. Use the system of equations to determine the point of intersection of lines l and p. l: y= 2x + 1 p: y= 1 2 x 3 B. Guided Practice: 1. 2x + 3y = x + 5y = 11 5x + 4y = 16 2x + 3y = 7 11
12 3. y = 3x 8 4. y = 4 x x 3 2y 2x 4y 6 Partitioning a Segment Notes ON GRAPH PAPER!!! 3.5 Proving Lines Parallel A. Opener: B. Definitions: 1. Converse of the Corresponding Angles Postulate: Example: 12
13 2. Parallel Postulate: 3. Kl 4. K 5. Kl 6. L; C. Examples: 1. Kij 2. 13
14 D. Guided Practice: 1. Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. OC 1.7 and 8.6 Proofs involving Parallel and Perpendicular Line and Coordinate Proofs A. Opener: 1. F 1.) Chapter 3 - OC Coordinate Proofs NOTES 14
15 4.) Given J(-3,1), K(3,3), L(2,-1), and M(-4,-3), prove JKL LMJ. 15
16 OC 1.7 and 8.6 Proof Notes (Chapter 3) *Note: Some of the fill in the blank proofs skip steps you have to work with what you are given. 1. Complete the Proof by filling in the blanks. Given: Prove: AF // CD DCA EBA AF // BE B C D E A Statements Reasons Given 2. CD // BE Substitution Property F 2. Complete the Proof by filling in the blanks. Given: 1 2 Prove: AC // BD A B C D Statements Reasons Transitive Property of Congruence B 3. Complete the Proof by filling in the blanks. Given: Prove: AB CB DB EB 1 4 DE// AC A D 1 2 E 3 4 C Statements Reasons Given , In a triangle, if opp. sides are congruent then opp. angles are congruent
17 17
18 3.6 Definitions Examples on graph paper. 1. Distance between a Point and a Line: 2. Perpendicular postulate: 3. Distance between Parallel Lines: 4. Equidistant: 5. Two lines Equidistant from a third: 18
2 and 6 4 and 8 1 and 5 3 and 7
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