GEOMETRY APPLICATIONS · 2010. 10. 12. · Day 5 - Chapter 3-6: Slopes of Parallel and Perpendicular Lines SWBAT: Use slopes to identify parallel and perpendicular lines Use the slope

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GEOMETRY

APPLICATIONS

Chapter 3: Parallel & Perpendicular Lines

Name:______________________________

Teacher:____________________________

Pd: _______

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Table of Contents

DAY 1: (Ch. 3-1 & 3-2) SWBAT: Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal. Pgs: 2-5

DAY 2: (Ch. 3-2) Calculate for missing angles when parallel lines are cut by a transversal Pgs: 6-10

DAY 3: Full Period Quiz: Day 1 to DAY 2

DAY 4: (Ch. 3-5) SWBAT: Calculate the slope of a line using the slope formula.

Pgs: 11-15

DAY 5: SWBAT: Use slopes to identify parallel and perpendicular lines

Pgs:16-19

Take Home Quiz: Day 4 to DAY 5

DAY 6: SWBAT: Graph and Write Equations of Lines given a Slope and Point

Pgs: 20-24

DAY 7: SWBAT: Write the equation of a line given two points on the line

Pgs: 25-27

DAY 8: SWBAT: Graph Lines in Slope – Intercept and Point – Slope Form

Pgs: 28-33

DAY 9: SWBAT: Graph and Write Equations of Parallel & Perpendicular Lines given a Slope and Point

Pgs: 34-37

DAY 10: Full Period Quiz: Day 6 to DAY 9

DAY 11: SWBAT: Graph the Solutions to Quadratic Linear Systems

Pgs: 38-43

DAY 12: SWBAT: Graph the Solutions to Quadratic Linear Systems Pgs: 44-45

DAY 13: Chapter 3 Practice Test DAY 14: Chapter 3 Test

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Day 1 - 3-1 & 3-2: Lines and Angles SWBAT: Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal. Warm – Up: Matching Column

supplementary angles

point

coplanar points

linear pair

points that lie in the same plane

two angles whose sum is 180°

the intersection of two distinct intersecting lines

a pair of adjacent angles whose non-common sides are opposite rays

Example 1: Lines

Term Description Example 1 Example(s) are coplanar

do not intersect

intersect at 90° angles

are not coplanar are not parallel do not intersect

planes that do not intersect

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Practice: Identify each of the following:

a. A pair of parallel segments

b. A pair of skew segments

c. A pair of perpendicular segments

d. A pair of parallel planes

Example 2: Angles A _____________________ is a line that intersects two coplanar lines at two different points.

Term Description Example 1 Example(s) Lie on:

the same side of the transversal t

on the same sides of lines r and s

Nonadjacent angles that lie on: opposite sides of the

transversal t between lines r and s

Lie on: opposite sides of the

transversal t outside lines r and s

Lie on: the same side of the

transversal t between lines r and s

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Practice

Identify each of the following:

a. A pair of alternate interior angles

b. A pair of corresponding angles

c. A pair of alternate exterior angles

d. A pair of same-side interior angles

Example 3: Line l and Line m are parallel. Find each missing angle.

Practice

Line l and Line m are parallel. Find each missing angle.

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Homework:

In the diagram, parallel lines AB and CD are intersected by a

transversal EF at points X and Y, m FYD = 123. Find AXY.

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Day 2 - Chapter 3 – 2 (Parallel Lines and Related Angles)

SWBAT: Calculate for missing angles when parallel lines are cut by a transversal

Warm – Up

Classify each pair of angles as alternate interior angles, alternate exterior angles,

same-side interior angles, corresponding angles, or vertical angles.

1) 2) 3)

4) 5) 6)

State the angle relationship that justifies each statement.

7) m 3 + m 4 = 180 _______________________

8) 1 5 _______________________

9) 3 5 _______________________

10) 5 8 _______________________

11) m 4 + m 5 = 180 _______________________

Find the m 1 and explain the angle relationship.

12. 13. 14

1

2

1

1

2

1

2

1

2 2

1

2

1 2

3 4

5 6

7 8

1

55 1

120

1

165

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Proving Lines Parallel

15. 16. 17.

Perpendicular Lines

18. Find the measure of b. 19. Find x and measure of b.

Algebra Related Questions

In the accompanying diagram, m ABC = (4x + 22) and m DCE = (5x) .

Part a: Which relationship describes ABC and DCE?

Part b: What is the value of x and what is m DCE?

b

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Homework

1) In the accompanying diagram, l ll m and m 1 = (3x + 40) and m 2 = (5x – 30) .

Part a: Which relationship describes 1 and 2?

Part b: What is the value of x and what is m 1?

2) In the accompanying diagram, l ll m and m 1 = (9x - 8) and m 2 = (x + 72) .


Part b: What is the value of x and what is m 2?

3) In the accompanying diagram, p ll q.

Part a: Which relationship describes the given angles?

Part b: What is the value of x?

1

2

l

m

1

2

l

m

5(x - 4)

(x + 12) p

q

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4) In the accompanying diagram, p ll q. If m 1 = (4x + 1) and m 2 = (5x – 10)


__________________________________________________________________________________________

__________________________________________________________________________________________


Part c: What is the m 2?

5) In the accompanying diagram, l ll m. If m 1 = (3x + 16) and m 2 = (x + 12)



Part c: What is the m 1 and m 2?

2

1

p

q

1

2

l

m

10

6) Find the m 6.

7) Find the measure of 3, 4, and 5.

8)

m 1 =

m 2 =

m 3 =

m 4 =

m 6 =

m 3 =

m 4 =

m 5=

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Day 4 - Chapter 3-5 Slope of a Line

SWBAT: Calculate the slope of a line using the slope formula.

Warm – Up

Solve for x.

The Slope “m” of a line passing through points (x1, y1) and (x2, y2) is the ratio of the difference in the y-coordinates to

the corresponding difference in the x-coordinates.

Symbols: m =

y

x

(x1, y1)

(x2, y2)

rise

run

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Example 1: Find the slope of (3,3) and (8,7).

Example 2: Find the slope of (2,3) and (-7,8).

Example 3: Find the slope of (-5,3) and (2,3).

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Finding Slope From Graphs and Tables. The graph or table shows a linear relationship. Find the slope.

4) 5)

6) 7)

Finding Slope from an Equation

8) Find the slope of the line described by 4x – 2y = 16.

9) Find the slope of the line described by 2x + 3y = 12.

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HOMEWORK:

1) Find the slope of (2, 5) and (8, 1).

2) Find the slope of (5, –7) and (6, –4).

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Finding Slope from an Equation

14. Find the slope of the line described by 6x – 3y = 18.

15. Find the slope of the line described by 3x + 4y = 16.

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Day 5 - Chapter 3-6: Slopes of Parallel and Perpendicular Lines

SWBAT: Use slopes to identify parallel and perpendicular lines

Use the slope formula to determine the slope of each line.

Pairs of Lines

Parallel Lines Perpendicular

Lines

Neither Coinciding Lines

Y = 5x + 8

Y = 5x - 4

Y = 2x + 6

Y = -½x - 4

Y = 3x – 5

Y = 5x + 2

Y = 2x – 4

Y = 2x - 4

Same Slope

different y-

intercept

Slopes are

Negative

Reciprocals

Different Slopes Same slope,

Same y-intercept

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Example 1

Find the slope of a line parallel to the graph of each equation.

a) y = -3

2x – 1 b) y = 4x - 1 c) 2x - 3y = 2

slope = _____ slope = _____ slope = _____

Independent Practice


a) y = -5

3x – 1 b) y = -3x - 1 c) 4x - 2y = 2


Example 2

Find the slope of a line perpendicular to the graph of each equation

a) y = 2x + 1 b) y = 7

2x - 4 c) 4x – 2y = 9


Independent Practice


a) y = -4x + 1 b) y = 3

5x - 4 c) 6x – 3y = 9


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Example 3 Determine whether the lines are parallel, perpendicular, coincide, or neither.

3x + 5y = 2 and 3x + 6 = -5y

Determine whether the lines are parallel, perpendicular, coincide, or neither.

a) y – 5 = 2x + 6 and y – 3 = – ½x b) 2y = 4x + 12 and 4x – 2y = 8

c) 2y – 4x = 16 and y – 10 = 2x - 2 d) y + 3 = ¾x + 16 and 3y = -4x - 9

Regents Question

Shanaya graphed the line represented by the equation y = 2x – 6.

A. Write an equation for a line that is parallel to the given line.

B. Write an equation for a line that is perpendicular to the given line.

C. Write an equation for a line that is identical to the given line but has different coefficients.

Challenge: Determine whether the lines are parallel, perpendicular, coincide, or neither.

y – (-3) = ¾(x + 16), 3y = -4x - 9

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Homework:


a) y = -8

3x – 1 b) y = -9x - 1 c) 10x - 2y = 2



a) y = -6x + 1 b) y = 4

5x - 4 c) 12x – 3y = 9


Determine whether the lines are parallel, perpendicular, coincide, or neither.

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Day 6 - Chapter 3-6: Equations of Lines Given Slope and Point

SWBAT: Graph and Write Equations of Lines given a Slope and Point

Warm – Up

1. Use the slope formula to determine the slope of the line that passes through A(3, 7) and B(-3, 1).

2. Graph the lines and use the slopes to determine whether they are parallel, perpendicular, or neither.

and for A(-2,5) and B(-3, 1), X(0, -2) and Y(1, 2)

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Writing Equations of Lines

Example 1

1) Write an equation of a line that passes through the given point with the given

slope:

(–1, 2) ; m = 2

Example 2


slope:

(5, -2) ; m =

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Practice


slope:

(2, -5) ; m = -2


slope:

(0, 3) ; m = 1

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slope:

(1, 2) ; m = -3


slope:

(-1, 5) ; m =

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Homework

Write an equation of a line that passes through the given point with the given slope:

1) (3, 0) ; m =

2) (2, 6) ; m =

3) (3, -1) ; m =

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Day 7 - Chapter 3-6: Equations of Lines Given Two Points

SWBAT: Write the equation of a line given two points on the line

Warm – Up

Find the slope of the line passing through the points (6,4) and (-2,-6).


Example 1

Write the equation of the line through the two points (1,1) and (2,3).

Example 2

Write the equation of the line through the two points (5,0) and (3,2)

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Practice

1. Write the equation of the line through the two points (8,5) and (9,6)

2. Write the equation of the line through the two points (0,0) and (-3,4)

3. Write the equation of the line through the two points (-3,-4) and (-5,-6)

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Homework

Write the equation of the line through the two points. 1. (3,1) and (6,2) 2. (-2,6) and (-4,5)

3. (1,-4) and (-2,8) 4. (-3,4) and (0,6)

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Day 8 - Chapter 3-6: Equations of Lines in Slope Intercept Form and Point Slope Form

SWBAT: Graph Lines in Slope – Intercept and Point – Slope Form

Warm – Up

1) Write an equation of a line that passes through the point (4,-2) with slope 1.

2) Write an equation of a line that passes through the points (–1, 0) and (1, 2).

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Linear Equations written in the form y = mx + b are called the slope-intercept form.

When an equation is written in this form, m is the ______ and b is the ____________.

Find the slope and the y-intercept, then graph.

a. y = -3

2x – 4 b. y =

5

1x + 2

slope = _________ slope = _________

y - intercept = _______ y- intercept = _______

c. y = 4x + 1 d. y = -2x

slope = _________ slope = _________


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Linear Equations written in the form y – y1 = m(x – x1) are called the point-slope form.


a. y + 3 = -2(x – 1) b. y - 3 = -2(x +4)

slope = _________ slope = _________


c. y + 4 = 4(x +2) d. y - 1 = 3

2(x + 3)

slope = _________ slope = _________


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Write an equation of each line below.

a. d.

b. e.

c. f.

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HOMEWORK


a. y = -3x + 4 b. y - 5 = 2(x +6)

slope = _________ slope = _________


c. x = 5 d. y + 4 = 3

2(x - 6)

slope = _________ slope = _________


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e. y -7 = x + 4 f. y = 2

slope = _________ slope = _________


g. y – x = -3 h. y = -3

1x + 1

slope = _________ slope = _________


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Day 9 –Chapter 3-6: Equations of Parallel & Perpendicular Lines

SWBAT: Graph and Write Equations of Parallel & Perpendicular Lines given a Slope and Point

Warm – Up


Example 1

Practice:

A) (-2, 2), y = 4x - 2

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Example 2

Practice:

B) (4, -2), y = -2x + 3

(4, 2), y = 1

2x + 1

C) (-8, -7), y = -x - 8

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D) (6, -2), y = -3x - 6

Challenge Problem

Wrap Up

List 3 things you learned today; 2 key terms you learned; and 1

question you have about today’s lesson.

3 2 1

(6, 4), y = 7x + 1

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Homework

1) 2)

3) 4)

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Day 11 - Chapter 3 – 6: Quadratic Linear Systems

SWBAT: Graph the Solutions to Quadratic Linear Systems

Warm – Up

1. Write an equation of the line that passes through the given point and is parallel to the graph of the

equation below.

2. Write an equation of the line that passes through the given point and is perpendicular to the graph of the

equation below.

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Example 2: Regents Questions

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Practice 3:

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Name: ______________________________________________________Date: ________ Ms. Williams

Homework

SWBAT: Solve Quadratic-Linear Systems

1.

2.

3.

4. What is the equation of a line that is perpendicular to -3y = 7x – 2 and passes through the

point (0, -8)?

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5.

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Day 12– Quadratic Linear Systems

Graph the lines and find the points of intersection.

1.

2.

3.

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4.

5. y = x2 - 9

y = -5

6. y = x2 – 2x – 3

x = 1

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GEOMETRY APPLICATIONS · 2010. 10. 12. · Day 5 - Chapter 3-6: Slopes of Parallel and Perpendicular Lines SWBAT: Use slopes to identify parallel and perpendicular lines Use the slope