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October 08, 2012 Geometry Ch. 3 Parallel and Perpendicular Lines Geometry 3-‐1: Parallel Lines and Transversals Warm-‐Up 1 2 62° 53° 3 1. What is the measure of angle 1? ______________ 2. What is the measure of angle 2? ______________ 3. What is the measure of angle 3? ______________ Vocab Word Parallel Lines Parallel Planes Skew Lines Transversal De,inition Example October 08, 2012 Consecutive Interior Angles Alternating Exterior Angles Alternating Interior Angles Corresponding Angles Identifying Angles 1. ___________________________ or ___________________________ 2. ___________________________ or ___________________________ • Special Case-‐ ___________________________ Assignment: 3-‐1 #’s 11-‐17, 22-‐28 even, 32-‐46 even, 48, 56, 62, 68-‐74 even October 08, 2012 Geometry 3-‐2: Angles and Parallel Lines Warm-‐Up Identify each pair of angles using the 4igure. 1. ∠7 & ∠9 _______________________________ 2. ∠11 & ∠13 _____________________________ a 3. b ∠8 & ∠4 ________________________________ c d Line b is parallel to line c. • All ________________ angles are __________________. • All ________________ angles are __________________. • _____________________ + _____________________ = ______________ In other words… Corresponding angles are _____________________. a b c Alternating interior angles are ___________________. Consecutive interior angles are ________________________. Alternating exterior angles are _____________________. * Also, If we have 2 parallel lines and a transversal perpendicular to one line, then _______________________ _____________________________________________________________________________________. Assignment: 3-‐2 #’s 5-‐11, 14-‐25, 32, 34, 45-‐52, 56 October 08, 2012 October 08, 2012 Geometry 3-‐3: Slopes of Lines Warm-‐Up 1. What is the +irst thing that comes to mind when you hear the word slope? ________________________________________________ 2. Simplify. a. b. Vocab Slope c. De(inition • Represented by ________ • ______________________ • ______________________ • ______________________ • Slopes of perpendicular lines are _____________________________. Slopes of parallel lines are ________________. Example October 08, 2012 Example Problems 1. Find the slope of the line. 2. Determine if AB and CD are perpendicular, parallel or neither when A (-‐2, 5), B (4, 7), C (0, 2), and D (8, -‐2). 3. Graph the line that contains Q (5, 1) and is parallel to MN when M(-‐2, 4) and N (2,1). Assignment: 3-‐3 #’s 16-‐38 even, 42, 44-‐46, 49, 52-‐60 even October 08, 2012 Geometry 3-‐4: Equations of Lines Warm-‐Up 1. Find the slope of line l. 2. What is the slope of a line parallel to line l. 3. What is the slope of a line perpendicular to line l. Vocab Word Y-‐Intercept Slope-‐Intercept Form Point-‐Slope Form De,inition Example October 08, 2012 Example Problems 1. Write an equation in slope-‐intercept form. and the y-‐intercept equals 4. 2. Write an equation in point-‐slope form that contains the point (-‐2, 6) and has a slope of -‐7. 3. Write an equation in slope-‐intercept form for line m. 4. Write an equation in slope-‐intercept form for a line that contains the points X (-‐3, -‐6) and Y (1, 6). Assignment: 3-‐4 #’s 2-‐12 even, 16-‐40 even, 46, 47, 54 October 08, 2012 Geometry 3-‐5: Proving Lines Parallel Warm-‐Up 1. Lines a & b are parallel. Fill in the measures of all the missing angles if m5 = 73 °. a ∠5 b How do you know if 2 lines are parallel? 2 Lines are parallel if… 1. Alternating exterior angles are _______________________. 2. Consecutive interior angles are ________________________. 3. Alternating interior angles are ________________________. 4. Corresponding angles are ____________________. 5. A transversal is __________________________ to both lines. 6. Slopes of both lines are ______________________. Assignment: 3-‐5 #’s 13-‐20, 26-‐28, 38, 39, 48-‐56 even October 08, 2012 Geometry 3-‐6: Perpendiculars and Distance Warm-‐Up Measure the following angles. a. In-‐Class Activity Assignment: 3-‐6 Wkst Ch. 3 Review Day 1: Pg. 167 #’s 1-‐40 Ch. 3 Review Day 2: Pg. 171 #’s 1-‐21, 24, 25 b. c.