Download Geometry Ch. 3 Parallel and Perpendicular Lines

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.