Geometry Unit 3 Note Sheets

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Date Name of Lesson

3.3 Slopes of Lines

3.3 Partitioning a Segment

3.4 Equations of Lines

Quiz

3.3 Introduction to Parallel and Perpendicular Lines

3.3 Slopes and Parallel Lines

3.3 Slopes and Perpendicular Lines

Slopes Puzzle

Practice Test

Unit 3 Test

Geometry Unit 3 Note Sheets

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3.3 Slopes of Lines Notes

What is slope? _____________________________________________________________________________

__________________________________________________________________________________________

Guided Practice

Find the slope of each line.

Geometry Unit 3 Note Sheets

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Your Turn

Find the slope of each line.

Guided Practice

Find the slope of the line containing the given points.

(6, −2) 𝑎𝑛𝑑 (−3, −5) (4, 2) 𝑎𝑛𝑑 (4, −3)

Your Turn

Find the slope of the line containing the given points.

(−3, 3) 𝑎𝑛𝑑 (4, 3) (8, −3) 𝑎𝑛𝑑 (−6, −2)

(5, 2) 𝑎𝑛𝑑 (4, −1) (9

2, 5) 𝑎𝑛𝑑 (

1

2, −3)

Geometry Unit 3 Note Sheets

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3.3 Partitioning a Segment Notes Can you find the midpoint of the line segment?

Now with the same line partition the segment in a ratio of 1:1.

Sometimes we need to break down segments into more than just two even pieces.

Guided Practice

1. Find the point, P, that lies along the direct line segment from A = -7 to B = 8 and partitions the segment

into the ratio of 2:3.

2. Find the point, P, that lies along the direct line segment from A = 9 to B = -4 and partitions

the segment into the ratio of 2:4. (use the vertical number line)

Your Turn

3. Find the point, P, that lies along the direct line segment from A = -6 to B = 8 and partitions

the segment into the ratio of 3:2.

Geometry Unit 3 Note Sheets

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Guided Practice

4. Given the points A(-3, -4) and B(5, 0), find the coordinates of the point P on directed line segment

AB that partitions AB in the ratio 2:3.

5. Given the points A(8, -5) and B(4, 7), find the coordinates of the point P on directed line segment

AB that partitions AB in the ratio 1:3.

Your Turn

6. Find the coordinates of point P that lies on the line

segment MQ , M(-9, -5), Q(3, 5), and partitions the

segment at a ratio of 2 to 5.

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3.4 Equations of Lines Notes Slope Point Slope Form Slope Intercept Form (h, k) Form

Depending upon what you are given you can use different equations for find the equation of a line.

Guided Practice

Write an equation in slope-intercept form of the line having the given slope and y-intercept.

𝑠𝑙𝑜𝑝𝑒: − 5, 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 − 2 𝑠𝑙𝑜𝑝𝑒: 5

11, (0, −3)

Your Turn

Write an equation in slope-intercept form of the line having the given slope and y-intercept.

𝑠𝑙𝑜𝑝𝑒: 12, 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 4

5 𝑠𝑙𝑜𝑝𝑒:

5

7, 𝑏: 8

Guided Practice

Write an equation in slope-intercept form of the line with the given slope and through the given point.

𝑚 = 2, (3, 11) 𝑚 = −4

5, (−3, −6)

Your Turn

Write an equation in slope-intercept form of the line with the given slope and through the given point.

𝑚 = 4, (−4, 8) 𝑚 =5

7, (−2, −5)

Guided Practice

Write an equation of the line through each pair of points in slope-intercept form.

(−12, −6) 𝑎𝑛𝑑 (8, 9) (0, 5) 𝑎𝑛𝑑 (3, 3)

Geometry Unit 3 Note Sheets

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Your Turn

Write an equation of the line through each pair of points in slope-intercept form.

(2, 4) 𝑎𝑛𝑑 (−4, −11) (−3, −2) 𝑎𝑛𝑑 (−3, 4)

Guided Practice

Find the equation of the graphed line.

Your Turn

Find the equation of the graphed line.

Geometry Unit 3 Note Sheets

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3.3 Introduction to Parallel and Perpendicular Lines Notes

Determine the slopes of the lines on each graph.

1.

2.

𝑚1 = __________ and 𝑚2 = __________ 𝑚1 = __________ and 𝑚2 = __________

3.

4.

𝑚1 = __________ and 𝑚2 = __________ 𝑚1 = __________ and 𝑚2 = __________

5.

6.

𝑚1 = __________ and 𝑚2 = __________ 𝑚1 = __________ and 𝑚2 = __________

7. Given that each set of lines above is parallel, what can you conclude about the slopes of parallel lines?

8. What happens if a line has the same slope and the same y-intercept?

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Determine the slopes of the lines on each graph. Then use a protractor to measure the angle of

intersection.

9.

10.

𝑚1 = __________ and 𝑚2 = __________

Angle of Intersection = _______

𝑚1 = __________ and 𝑚2 = __________

Angle of Intersection = _______

11.

12.

𝑚1 = __________ and 𝑚2 = __________

Angle of Intersection = _______

𝑚1 = __________ and 𝑚2 = __________

Angle of Intersection = _______

13.

14.

𝑚1 = __________ and 𝑚2 = __________

Angle of Intersection = _______

𝑚1 = __________ and 𝑚2 = __________

Angle of Intersection = _______

15. What do you notice about each set of slopes in the graphs above?

16. What do you notice about the angles of intersection in the graphs above?

17. What kind of lines would you classify these as? Explain.

Geometry Unit 3 Note Sheets

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3.3 Slopes and Parallel Lines Notes What is the connection between slope and parallel lines?

Slope is useful for determining whether two lines are parallel.

Slope Criterion for Parallel Lines

Because the theorem above has a biconditional (if and only if) you can use it in either “direction”.

Recall the different ways to write equations of lines.

Slope Intercept Form Point Slope Form (h, k) Form

Geometry Unit 3 Note Sheets

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Your Turn

Guided Practice

Your Turn

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

Geometry Unit 3 Note Sheets

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3.3 Slopes and Perpendicular Lines Notes What is the connection between slope and perpendicular lines?

Slope is useful for determining whether two lines are perpendicular.

Slope Criterion for Parallel Lines

Because the theorem above has a biconditional (if and only if) you can use it in either “direction”.

Geometry Unit 3 Note Sheets

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Guided Practice

The line with the given equation is perpendicular to line j at point R. Write an equation of line j.

1. 2.

Your Turn

3. 4.

Guided Practice

5.

Your Turn

6.

7.