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Name__________________________________________Block_______________ Ch 3: Parallel and Perpendicular Lines

PRACTICE PROBLEMS

Assignment Score Learning Target(s)

Notes What am I confident about?

Where do I need to spend more time? Am I weak on a prerequisite skill?

What am I going to do if I am weak?

3.1 and 3.2 23

3.1- 3.3 34

3.4 and 3.5 22

Review Worksheet #1

45

Review Worksheet #2

17

Learning Targets:

Identify angle pairs formed by three intersecting lines Use angles formed by parallel lines and transversals

Use angle relationships to prove that lines are parallel Find and compare slopes of lines

Find equations of lines

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Unit 3 Syllabus: Ch 3 Parallel and Perpendicular Lines Block Date Topic Homework

16 B 10/16 A 10/17

3.1 Identifying Lines and Angles 3.2 Angle Relationships and Parallel Lines

Worksheet: 3.1 and 3.2 Identifying Lines and Angle Relationships

17 B 10/20 A 10/21

3.3 Proving Lines Parallel Worksheet: 3.3 Proving Lines Parallel

18 B 10/22 A 10/23

Quiz 3.1-3.3 Khan Academy

19 B 10/24 A 10/27

3.4 Slope of Lines 3.5 Writing Equations of Lines

Worksheet: 3.4 Slope of Lines 3.5 Writing Equations of Lines

20 B 10/28 A 10/29

Review Ch 1 and 2 for Quarter Test Review Worksheet—Separate from packet

21 B 10/30 A 10/31

Quarter 1 Benchmark Test Review Worksheet #1

NEW QUARTER 1

B 11/5 A 11/6

Review Day Ch 3 Review Worksheet #2

2 B 11/7 A 11/8

Ch 3 Test Khan Academy

***Syllabus subject to change due to weather, pep rallies, illness, etc Need Help? Email your teacher to set up a time before or after school! Peer Tutoring is available through Mu Alpha Theta is Monday, Tuesday, Thursday, and Friday mornings in L403. Need to make up a test/quiz? Math Make Up Room is open Tuesday, Thursday, and Friday mornings and Monday, Wednesday, and Thursday afternoons.

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HW: 3.1- 3.2: Identify Pairs of Lines, Use Parallel Lines #10-13 Use the diagram

10. Name a pair of parallel lines. ________________ 11. Name a pair of perpendicular lines. _____________ 12. Is PN KM

suur suuurP ? Explain

13. Is PR NP⊥

suur suur? Explain.

23

Usethediagramofthefireescapetodecidewhetherthestatementistrueorfalse.

6.Theplanescontainingtheplatformsoutsideofthewindowsareparalleltotheground.______________7.Theplanescontainingthestairs(butnottheladder)areparalleltoeachother.________________8.Theplanescontainingtheplatformsoutsideofeachpairofwindowsareperpendiculartotheplanescontainingthewallsthathave6windows.________________9.Theplanescontainingthewallswith6windowsareperpendiculartotheplanescontainingthewallsthathaveninewindows.________________

Thinkofeachsegmentinthediagramaspartofaline.Completethestatementwithparallel,skew,orperpendicular.

1. _____________________.2. _____________________.3. _____________________.4.PlaneWZRandplaneSYZare____________________.5.PlaneRQTandplaneYXWare___________________.

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#14-17 Identify all pairs of angles of the given type. 14. Corresponding 15. Alternate Interior

16. Alternate Exterior 17. Consecutive Interior

For numbers 18-20, find m∠ 1 and m ∠ 2

18. 19. 20.

m ∠ 1______________ m ∠ 1______________ m ∠ 1_______________

m ∠ 2______________ m ∠ 2______________ m ∠ 2_______________

For numbers 21-23, solve for x .

21. 22. 23.

X= X= X=

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HW3.1-3.3Review:PairsofLines,ParallelLines,ProveParallelClassifyeachpairofanglesascorresponding,alternateinterior,alternateexterior,consecutiveinterior,orconsecutiveexterior.Findthevaluesofxandy.7. 8. 9.

10. 11. 12.

34

6

Whichlinesorsegmentsareparallel?(Besuretolistsome,all,ornoneofthepairsbytheirnames.)Justifyyouranswerwithatheorem.(ie.A//Bbecauseofthealt.int.anglesarecongruent)13. 14. 15.Isitpossibletoprovethatlineareparallel?Ifso,statethepostulateortheoremyouwoulduse.16. 17. 18.19. 20. 21.

108

108

t

m

l

t

l

m

65

65

t

l

m

100

72

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Findthevalueofxthatmakesm||n.22. 23. 24.25.Findthevalueofxthatmakesa//b.26.Findthevalueofythatmakesa//c.

b

a

c

3x+60

6x+15

15y

l

27

28

29

30

31

32

33

34

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HW: 3.4 and 3.5 Find and Use Slopes of Lines and Equations of a line

Match the description of the slope of a line with its graph.

______1.) m is positive

______2.) m is negative ______3.) m is zero ______4.) m is undefined Find the slope of the line using the graph. 5. 6. 7. 8.) Describe and correct the error in finding slope of the line. For each equation, rewrite in slope-intercept form, then state m and b. 5. 9x + 2y = -14 6. 4y – 2x = 3 7. 6x = 10y +2

A B C D

25

9

Determine the slope of the line passing through each pair of points. h: ( 5, 5) and (4, 7) l: (10, 8) and (4, 8) t: (-6, 3) and (0, -4) r: (6,-2) and (7, -4) s: (10, 2) and (17, 8)

8. Which two lines are parallel? 9. Are any of these lines perpendicular? Find the slope of each line. Are the lines parallel? 10. 11. Find the slope of each line. Are the lines perpendicular? 12. 13. Write the equation of the line that passes through the given y-intercept and has the given slope.

14. m = 12, b = 9 15. m = −35

, b = 1 16.

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Write the equation of the line that passes through the given point and given slope.

17. Passes through (6, -2) and slope is 4. 18. Passes through (0, 3) and slope is 34

Write the equation of a line given two points. 19. Passes through (7, 8) and (-3, 0) 20. Passes through (5, 1) and (-7,3) 21. Write the equation of a line that: 22. Passes through (8, 1) and is 23. Passes through (6, -2) and is

parallel to = +1 15

y x perpendicular to -x + 2y = 10

24. Passes through P and is parallel to AB

sur. 25. Passes through P and is perpendicular

to ABsur

.

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HW: Review Worksheet #1 Point E is between D and F on DF . Use the given information to write an equation in terms of x. Solve the equation. Then find DE and DF. 1.

2. Line AB bisects CDa point B. Find CD if BD = 358

inches.

3. Find m∠DEG and m∠GEF. 4. Find the measure of each angle in the diagram. 5. Classify the angle pair as corresponding, alternate interior, alternate exterior or consecutive interior angles. a. d. b. e. c. f.

45

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Find the angle measure. Tell which postulate or theorem you use. 6. 7. 8. 9. Find each missing angle. 10. 11. 12. Tell whether the lines through the given points are parallel, perpendicular, or neither. 13. 14. Find the value of x and y. 15.

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Find the value of x that makes m n . 16. 17. Write the equation of the line that goes through the given point and has the given slope. 18. 19. Determine if the lines can be proven parallel. If so, provide a reason. Or, state cannot be determined. 20. 21. 22. 23. 24. 25. 26. 27 28. For 33, which pair of lines are parallel? Find the slope that goes through the following points. 29. A(4, 9) and B(4, -6) 30.

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Write the equation of the lines with the given information. (You may count or calculate slope.) 31. 32. Write the equation of the line that goes through the points (-2, 3) and (4, 3). Write the equation of the line that is parallel to the given line and passes through P. 33. Write the equation of the line that is perpendicular to the given line and passes through P. 34. Find the equation of the line that is perpendicular to AB and passes through P. Then, graph the line. 35.

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Graph the line that is parallel to AB and passes through P. 36. 37. Are the following line parallel, perpendicular, or neither? k: y = 3 5

2x− − j: 3 9

2x y− + =

38. Determine if DC is congruent toNM given the following coordinates? DC : D(-9, 5) and C(-5, 12) NM : N(0, 3) and M( -7, -1) 39. Find the midpoint of DC given: D(-9, 5) and C(-5, 12) In the following diagrams, m is parallel to n. Find the value of x. 40. 41. 42. 43. 44. 45.

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HW: Review Worksheet #2 #1-4: Use the given diagram to answer the following questions.

A Parallel B Perpendicular C Skew D None of these _______ 1. Classify the lines DGFE and .

_______ 2. Classify the lines BCAD and .

_______ 3. Classify the lines .and EHAD

_______ 4. Classify the lines .and DCAD #5- 8: Use the diagram for the following questions.

_______ 5. ∠4 and _____ are corresponding angles.

A ∠7 B ∠5 C ∠3 D ∠8 _______ 6. ∠3 and _____ are consecutive interior angles. A ∠8 B ∠5 C ∠6 D ∠3 _______ 7. ∠3 and ∠6 are __________ angles. A consecutive interior B alternate interior

C corresponding D vertical _______ 8. ∠6 and ∠7 are __________ angles. A vertical B consecutive interior C corresponding D alternate interior _______ 9. In the diagram ml , find the value of x.

A 138° B 128° C 118° D 62°

_______ 10. In the diagram ml , find the value of x.

A 122° B 68° C 58° D 48°

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#11-13: Answer each question, SHOW ALL WORK, and justify your work by stating the postulate or theorem that allowed you to set up an equation. _______ 11. In the diagram ml , find the value of x. A 9.5 B 76

C 33 D 10.75 reason:____________________________ _______ 12. In the diagram find the value of x that would make ml . A 65 B 45

C 22.5 D 60 reason:____________________________ _______ 13. In the diagram find the value of x that would make ml . A 21 B 24

C 41 D 96 reason:____________________________ #14-17: Short Answer- Show all work and circle your final answer.

14. Find the slope of the line that passes 15. Given that line 1 passes through (-2, 1) through ( ) ( )6,62,2 and− . and (1, -1) and line 2 passes through (1, 3) and (4, 1). Determine if the lines are parallel,

perpendicular, or neither. 16. Write an equation of a line that is 17. Write an equation of a line that is

parallel to 52 +−= xy and passes perpendicular to 323

−−= xy and passes

through ( )2,3− . through ( )2,5− .