Unit 3 Parallel and Perpendicular Lines, Study notes of Reasoning

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Geometry

Unit 3

Parallel and Perpendicular Lines

Name:________________________________________________

Geometry

Chapter 3 – Parallel and Perpendicular Lines

_*In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *_

1.____ (3-1) Parallel Lines and Transversals – Day 1 Page 129 – 130 # 22 – 46 even

2. ____ (3-2) Angles and Parallel Lines – Day 1 Page 136 – 137 # 14 – 25, 32 – 36 3. ____ Wrap-Up (3-1) and (3-2) 3 - 1/3-2 Practice Worksheet and 3-2 Application WS

4.____ (3-3) Slopes of Lines – Day 1 Page 142 # 16 – 38 even

5. ____ (3-3) Slopes of Lines – Day 2 3 - 3 Practice Worksheet and 3-3 Application WS 6. ____ (3-4) Equations of Lines – Day 1 Page 148 # 15 – 43 odd, 46 – 49 7. ____ (3-4) Equations of Lines – Day 2 3 - 4 Practice Worksheet and 3-4 Application WS 8. ____ (3-5) Proving Lines Parallel – Day 1 Page 155 # 13 – 24, 26 – 31, 38, 39 9. ____ (3-5) Proving Lines Parallel – Day 2 Section 3-5 Practice Worksheet

10. ____ Chapter 3 Review WS

Date: _____________________________

Section 3 – 1: Parallel Lines and Transversals

Notes

Parallel Lines: coplanar lines that do not ____________________

 Symbol:

 Ex:

Parallel Planes: ______________ that do not ___________________

 Ex:

Skew Lines: lines that do not ___________________ and that are not ________________

Example #1: Refer to the figure on the right.

a.) Name all planes that are parallel to plane AEF.

b.) Name all segments that intersect AF.

c.) Name all segments that are parallel to DC.

d.) Name all segments that are skew to AD.

Transversal: a line that intersects Ex:

_________ or more lines in a plane

at different _______________

Example #2: Identify the pairs of lines to which each given line is a transversal.

a.) p b.) r

c.) q d.) t

Key Concept (Transversals and Angles):

Transversal p intersects lines q and r.

a.) Exterior Angles

b.) Interior Angles

c.) Consecutive Interior Angles

d.) Alternate Exterior Angles

e.) Alternate Interior Angles

f.) Corresponding Angles

Discovering Properties of Parallel Lines

Directions:

**1. Using the lines on a piece of paper as a guide, draw a pair of parallel lines.

2. Draw a transversal intersecting the parallel lines and number the angles formed from 1 to 8.
3. Use a protractor to measure each of the numbered angles and fill in the chart below.**

Angle Measure Angle Measure

Using the table and your picture, make as many different observations as possible. (Make sure to include

all eight angles)

Date: _____________________________

Section 3 – 2: Angles and Parallel Lines

Notes

IF TWO PARALLEL LINES ARE CUT BY A TRANSVERSAL, THEN:

 By the Corresponding Angles Postulate each pair of corresponding angles is

_____________________.

 By the Alternate Interior Angles Theorem each pair of alternate interior angles is

_____________________.

 By the Alternate Exterior Angles Theorem each pair of alternate exterior angles is

_____________________.

 By the Consecutive Interior Angles Theorem each pair of consecutive interior

angles is __________________________.

Example #1: In the figure, m ^^3 ^110 and m ^^12 ^55. Find the measure of each

angle.

a.)  1 b.)  6

c.)  2 d.)  10

e.)  13 f.)  15

CRITICAL THINKING

For questions 1 and 2, refer to the picture at the right.

1.) Determine whether  1 is always, sometimes, or

never congruent to ^2. Explain.

2.) Determine the minimum number of angle measures you would have to know to

find the measures of all of the angles in the figure. Explain your reasoning.

Example #3: Find the slope of l, m, and n. Compare the slopes of each.

Two nonvertical lines have the _________ slope if and only if they are ___________.

Two nonvertical lines are _________________ if and only if the product of their slopes is _________.

Example #4: Determine whether ⃖ ⃗ and ⃖ ⃗ are parallel, perpendicular, or neither.

a. F(1, - 3), G(-2,-1), H(5,0), J(6,3)

b. F(4,2), G(6, - 3), H(-1, 5), J(-3, 10)

CRITICAL THINKING

1.) Find the Error: Curtis and Laura calculated the slope of a line containing A (15, 4)

and B (-6, - 13). Who is correct? Explain your reasoning.

2.) The maximum recommended slope of a wheelchair ramp is 1/12. A business is

installing a wheelchair ramp that rises 22 inches over a horizontal length of 228 inches.

Is the ramp steeper then recommended? Be sure to show all of your work, and explain

your reasoning.

Date: _____________________________

Section 3 – 4: Equations of Lines

Notes

Slope-Intercept Form –

Example #1: Write an equation in slope-intercept form of the line with slope of – 4 and y - intercept

of 1.

Example #2: Write an equation in slope-intercept form of the line with slope 5 and a point

at (0, - 8).

Example #3: Write an equation in slope-intercept form of the line with slope – 2 and a point

at (-3, 6).

Point-Slope Form –

Example #4: Write an equation in point-slope form of the line whose slope is 5

 that contains

Example #5: Write an equation in slope intercept form for a line containing (4, 9) and (-2, 0).

Example #6: Write an equation in slope-intercept form for a line containing (1, 7) that is

perpendicular to the line 1 2

y   x .