Questions

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) Answer the following questions: When discussing the slope of a line, (a) what is the vertical rise? (b) what is the horizontal run?

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

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

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

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

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

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

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9) Will this formula work for determining the slope of a line? Please give a rationale for your answer. You may refer to one or more sets of points given in the previous problems as test points to explain your answer or you may give a more general answer.

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

a.) 0/5 = 0, 5/0 = 0

b.) 0/5 is undefined, 5/0 is undefined

c.) 0/5 is undefined, 5/0 = 0

d.) 0/5 = 0, 5/0 is undefined

11) 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?

a.) 0, vertical line

b.) 0, horizontal line

c.) undefined, vertical line

d.) undefined, horizontal line

12) 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?

a.) 0, vertical line

b.) 0, horizontal line

c.) undefined, vertical line

d.) undefined, horizontal line

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

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

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16) This line has what kind of slope?

a.) positive

b.) negative

c.) zero

d.) undefined

17) This line has what kind of slope?

a.) positive

b.) negative

c.) zero

d.) undefined

18) This line has what kind of slope?

a.) positive

b.) negative

c.) zero

d.) undefined

19) This line has what kind of slope?

a.) positive

b.) negative

c.) zero

d.) undefined

20) Postulate 8-A: Two non-vertical lines have the same slope if and only if they are __________.

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21) Postulate 8-B: Two non-vertical lines are perpendicular if and only if the product of their slopes is __________.

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

a.) Their products equal –1.

b.) There is no connection.

c.) They are the same value.

d.) Their products equal 1.

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

a.) Their products equal –1.

b.) There is no connection.

c.) They are the same value.

d.) Their products equal 1.

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

True

False

25) Which statement best describes the two given lines?

a.) The lines are parallel.

b.) The lines are perpendicular.

c.) The lines are intersecting non-perpendicular lines.

26) Which statement best describes the two given lines?

a.) The lines are parallel.

b.) The lines are perpendicular.

c.) The lines are intersecting non-perpendicular lines.

27) 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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28) 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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29) Answer the following questions: (a) If a line is parallel to the x-axis, what is the value if its slope? (b) If a line is parallel to the y-axis, what is the value of its slope?

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30) On graph paper, plot these points and draw the given lines. Are the lines parallel or perpendicular? Support your answer by explaining how you determined the solution.

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31) Find “x” so that a line drawn through the given points has the given slope. (Sketching the problem may be helpful.)

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32) 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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33) 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 8-C.)

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34) In the previous construction, how many lines may be drawn through point P and also be parallel to line “m”? (Hint: refer to postulate 8-D.)

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35) Fill in the blank. Theorem 8-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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36) Write a proof for Theorem 8-B using the figure below as a reference. For a model, refer to Theorem 8-A in the unit area link to “Theorems about Parallel Lines”. You may write a paragraph proof or type up a formal proof and attach it below.

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37) Copy or print Theorem 8-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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38) Fill in the blank. Theorem 8-D: If two lines in a plane are __________ to the same line, then the lines are parallel.

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39) What theorem supports the following statement?

a.) Theorem 8-A

b.) Theorem 8-B

c.) Theorem 8-C

d.) Theorem 8-D

40) What theorem supports the following statement?

a.) Theorem 8-A

b.) Theorem 8-B

c.) Theorem 8-C

d.) Theorem 8-D

41) According to theorem 8-D, if line “t” is perpendicular to line “v” and angle 9 measures 90 degrees, then line “v” is parallel to what line?

a.) line “m”

b.) line “n”

c.) line “w”

42) 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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43) What is the value of “x”? Explain your solution.

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44) 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?

True

False

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

True

False

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

a.) AP

b.) BP

c.) CP

d.) DP

e.) EP

47) 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.

a.) parallel

b.) perpendicular

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

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49) In the figure below points S (–3, –1) and R (–2,2) line on line SR. Points T(1,1) and V(0, –2) line on line VT. (a) What is the slope of line TV? (b) What is the slope of line RS? (c) Are lines TV and RS parallel? Please explain.

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50) In the figure in the previous problem, draw segment SV. (a) What is the slope of segment SV? (b) What is the relationship between segments SR and SV? (c) What is the distance between lines SR and VT? (Hint: use the distance formula.)

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