MATH Integrated Math II  - Unit 11: Parallel and Perpendicular Lines
Slope of a Line

1) Complete this statement: The slope of a line describes the _________________ of the line. The slope is the ratio of the _________________ to the _________________.

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2) What does the Greek symbol shown below represent and how is it read?

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3) What is the slope of the line in the figure?

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4) State the letter of the correct formula for determining the slope of a line when given two points.

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For the next three problems calculate the slope. Express the answers as a fraction in simplified form.

5) Calculate the slope of a line that contains the following points: (–4,2) and (3,6).

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6) Calculate the slope of a line that contains the following points: (–7,–9) and (8, 11).

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7) Calculate the slope of a line that contains the following points: (–5,–4) and (–8,6).

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Four Types of Slopes

8) Which of the following statements is true about the two fractions given below?

9) Calculate the slope of a line that contains the following points: (5,–7) and (8,–7), and then draw the line. What is the slope and type of line?

10) Calculate the slope of a line that contains the following points: (6, –2) and (6, 4), and then draw the line. What is the slope and type of line?

For the next three problems, graph the point on graph paper in an x-y plane; and then, count out the rise/run of the given slope to determine a second point on the line.

11) What is the ordered pair of a second point on a line that contains the point and has the slope shown below?

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12) What is the ordered pair of the second point you used to graph the line?

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13) What is the ordered pair of the second point you used to graph the line?

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For the next four problems, determine the type of slope of the line displayed in the grid.

14) This line has what kind of slope?

15) This line has what kind of slope?

16) This line has what kind of slope?

17) This line has what kind of slope?

Slopes of Parallel and Perpendicular Lines

Complete the next two questions by filling in the blanks.

18) Postulate 11-A: Two non-vertical lines have the same slope if and only if they are __________.

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19) Postulate 11-B: Two non-vertical lines are perpendicular if and only if the product of their slopes is __________.

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20) What is true about the slopes of parallel lines?

21) What is true about the slopes of perpendicular lines?

22) True or False. Perpendicular lines have opposite reciprocal slopes.

23) Which statement best describes the two given lines?

24) Which statement best describes the two given lines?

25) If a line that has a slope of 7/8 is parallel to a second line, what is the slope of the second line?

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26) If a line has a slope of 3/8 and is perpendicular to a second line, what is the slope of the second line?

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Constructions of Angles and Parallel Lines

Activity: Print out the angle and ray below. Construct angle CAB on ray A, so that it is congruent to angle GFK. Use a compass to make the construction and follow the steps in the unit area link to “Constructions of Angles and Parallel Lines”.

27) The diagrams for steps #5 and #6 of constructing congruent angles are shown below. In the following paragraph, fill in the missing phrase that is crucial when constructing congruent angles: After completing step #5, ________________________ and move over to ray NT. Place the metal point of the compass at point T and draw a small arc that intersects the larger arc. Name the point of intersection, point R.

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28) The diagram for step #3 of constructing parallel lines is shown below. In this step, two congruent angles are being constructed. What kind of angles are angles 1 and 2? (Hint: refer to postulate 11-C.)

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29) In the previous construction, how many lines may be drawn through point P and also be parallel to line “m”? (Hint: refer to postulate 11-D.)

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Theorems about Parallel Lines

30) Fill in the blank. Theorem 11-A: If two lines in a plane are cut by a transversal and the alternate interior angles are congruent, then the lines are __________.

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31) Fill in the blanks in the following paragraph proof of theorem 11-B: We will say that it is given that angles 8 and 1 are congruent because they are alternate exterior angles. Angle 1 is congruent to angle 4 because they are __________ angles. Since angle 4 is congruent to angle 1 and angle 1 is congruent to angle 8, we can apply the __________ property and say that angle 8 is congruent to angle 4. Angles 4 and 8 are congruent __________angles; thus, lines “m” and “n” are parallel based on postulate _____.

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32) Copy or print Theorem 11-C and complete the proof by filling in the blanks. State the answers by giving the number of the statement or reason, and then the answer.

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33) Fill in the blank. Theorem 11-D: If two lines in a plane are __________ to the same line, then the lines are parallel.

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Refer to the figure below to answer the next two questions.

34) What theorem supports the following statement?

35) What theorem supports the following statement?

36) According to theorem 11-D, if line “t” is perpendicular to line “v” and angle 9 measures 90 degrees, then line “v” is parallel to what line?

37) In the figure below, parallel lines are cut by a transversal. Refer to the figure and the information to answer the following questions: (a) What is the value of “x”? (b) What is the value of “y”? (c) What is the measure of angle 2?

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Constructions with Perpendicular Lines

Activity: Print out the figure below and then use a compass to construct a perpendicular bisector of the given line.

38) True or False? In the previous construction, there is exactly one point above the segment TV that can be used to construct the perpendicular line?

Activity: Print out the figure below and then use a compass to construct a perpendicular line from point Z to segment KL.

39) True or False? In the previous construction, there is exactly one line that can be drawn through point Z and perpendicular to segment KL.

Distance between a Point and a Line

40) In geometry, which line segment represents the distance between point P and line AE?

41) Select the term that completes the following statement: The distance from a point which is not on a line and a line is the length of a line segment that is _______________ from the point to the line.

42) In the figure below, which line segment represents the distance between segment TN and Point S?

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