section i name the three ways to prove that parallel … 3...section i –name the three ways to...

Geometry/Trig 2 Name: __________________________

Unit 3 Review Packet Date: ___________________________

Section I – Name the three ways to prove that parallel lines exist.

1. ____________________________________________________________________

2. ____________________________________________________________________

3. ____________________________________________________________________

4. ____________________________________________________________________

5. ____________________________________________________________________

Section II – Identify the pairs of angles. If the angles have no relationship, write none.

1. 7 & 11 _________________________________

2. 3 & 6 _________________________________

3. 8 & 16 ________________________________

4. 2 & 7 _________________________________

5. 3 & 5 _________________________________

6. 1 & 6 __________________________________

7. 1 & 6 __________________________________

8. 1 & 4 __________________________________

Vertical angles are ______________________________________

If two parallel lines are cut by a transversal, then corresponding angles are ___________________

If two parallel lines are cut by a transversal, then alternate interior angles are _________________

If two parallel lines are cut by a transversal, then alternate exterior angles are ________________

If two parallel lines are cut by a transversal, then same side interior angles are ________________

If two parallel lines are cut by a transversal, then same side exterior angles are ________________

If two lines are perpendicular, then they form ______________, adjacent angles.

If two lines are parallel, then they are _________________ (A, S, N) skew.

A regular polygon is ________________ (A,S,N) equilateral.

The acute angles of a right triangle are ___________ (A,S,N) supplementary.

Section III – Fill In


Unit 3 Review Packet – Date: ___________________________

Section IV – Determine which lines, if any, are parallel based on the given information.

1 2

3 4

6

87

5

9 10

11 12

14

1615

13b

a1.) m1 = m9 _________________________

2.) m1 = m4 _________________________

3.) m12 + m14 = 180 _________________________

4.) m1 = m13 _________________________

5.) m7 = m14 _________________________

6.) m13 = m11 _________________________

7.) m15 + m16 = 180 _________________________

8.) m4 = m5 _________________________

Section IV – Determine which lines, if any, are parallel based on the given information.

312

45

6

87

9

10

111213

s

t

mkb

a

14

15

c d

1. m1 = m4 ___________________

2. m6 = m8 __________________

3. 1 and 11 are supplementary _______________

4. a ^ t and b ^ t ___________________________

5. m14 = m5 ______________________________

6. 6 and 7 are supplementary ________________

7. m14 = m15 ____________________________

8. 7 and 8 are supplementary _________________

9. m5 = m10 ______________________________

10. m1 = m13 ______________________________


Unit 3 Review Packet – page 3 Date: ___________________________

Section V – Solve each Algebra Connection Problem.

1. 2.

4.3.

75

30

5x

x = _______

y = ________

w = _______

x = _______

y = _______

z = _______

x = _______

y = _______

37 2y

z + 57

w

x

4x - 5 23y

65 125

y

x + 12

6x 8x + 1

x = _______

6.5.4x + 13 4x + 25

6x6x

4x + 25 4x + 13

x = _______

A B

CD

x = _______

Is AB // DC? __________

Is AD // BC? __________

80

5x 4x + 17

83

10) ____ scalene right

11) ____ scalene acute

12) ____ scalene obtuse

13) ____ isosceles right

14) ____ isosceles acute

15) ____ isosceles obtuse

A) B) C)

D) E) F)

40°

80° 60°

80°

50° 50°

35°

35°

105°

45°

30°

Section II – Match each classification with the triangle that BEST suits it.

Number of Sides

Name of polygon

Sum of interior angles.

Measure of each interior

angle if it was a regular

polygon

Sum of the

Exterior Angles

Measure of each exterior angle if it

was a regular polygon.

Number of Diagonals that can be drawn.

3

4

5

6

7

8

9

10

n

Section II – Complete the chart.

Section VI – Answer each question regarding the given polygon.

30) Given a regular polygon with 6 sides, find:

31) The sum of the interior angles of this polygon is 900.

a) Name:

b) Sum of Interior Angles:

c) Sum of Exterior Angles:

d) Each Interior Angle:

e) Each exterior angle:

How many sides does this polygon have?

_______________________

What is the name of this polygon?

______________________

How many diagonals can be drawn in this polygon?

__________________

Section VII – Classify each polygon as convex or not convex; regular or irregular; name the polygon by number of sides. (Circle or fill in the appropriate answers).

34) 35) 36)

Convex OR Not Convex

Regular OR Irregular

Name: ____________________



Name: ____________________



Name: ____________________

32. ) Given a regular polygon with 6 sides, find:

a) Name:

b) Sum of Interior Angles:

c) Sum of Exterior Angles:

d) Each Interior Angle:

e) Each exterior angle:

32a.) Find the measure of one interior angle of a regular polygon with 18 sides:

b.) If each exterior angle of a regular polygon is 40 degrees, how many sides does it have?

c.) If each interior angle of a regular polygon is 72 degrees, how many sides does the polygon have?

Section V - Proofs

Statements Reasons

J

G K

IH

1. Given: GK bisects JGI; m3 = m2

Prove: GK // HI

1.

2.

3.

4.

5.

1. Given

2.

3. Given

4.

5.


Unit 3 Review Packet – Page 3 Date: ___________________________

2

1

Statements Reasons

2. Given: AJ // CK; m1 = m5 Prove: BD // FE

1 2 3

4

5

A C

D

EF

B

J K

3

Statements Reasons

3. Given: a // b; 3 @ 4 Prove: 10 @ 11

3 4

5

6

7 8

910

2

b

a

c d


Unit 3 Review Packet – Page 4 Date: ___________________________

1 3

54

6 7

28a

b

4. Given: 1 and 7 are supplementary.

Prove: m8 = m4

Statements Reasons


Unit 3 Study Guide – Parallel Lines & Proofs

Section 3-1

Definitions:

Parallel Lines, Skew Lines, Parallel Planes, Parallel Line and Plane, Transversal, Alternate Interior Angles, Alternate Exterior Angles, Same Side Interior Angles, Corresponding Angles

Know How To:

1) Name figures described above.

2) Find the intersection of two figures.

3) Identify special pairs of angles

Suggested Exercises:

p. 75 #1-19; p. 76 #1-17; p. 77 #23-39

Section 3-2

Postulates and Theorems:1. If two parallel lines are cut by a transversal, then corresponding angles are congruent.

2. If two parallel lines are cut by a transversal, then alternate interior/exterior angles are congruent.

3. If two parallel lines are cut by a transversal, then same side interior angles are supplementary.

4. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

Know How To:

1) Use the statements above to complete proofs.

2) Find angle measures using the statements above.

3) Solve algebra connection problems using the statements above.

Suggested Exercises: p. 80 #1-13; p. 80-81 #1-16

Section 3-3

Know How To:

1.) Use these statements to complete proofs.

2.) Use these rules to determine whether given lines are parallel.

Suggested Exercises: p. 86 #1-11; p. 87 #1-19; p. 88 #24-26. p. 89 #1-16

You will be asked to name the 5 ways to prove that two lines are parallel. You may NOT use shorthand or abbreviations. They are:

1.) If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

2.) If two lines are cut by a transversal and alternate interior/exterior angles are congruent, then the lines are parallel.

3.) If two lines are cut by a transversal and same side interior/exterior angles are supplementary, then the lines are parallel.

4.) If two lines are parallel to a third line, then the lines are parallel.

5.) If two lines are perpendicular to a third line, then the lines are parallel.

section i name the three ways to prove that parallel … 3...section i –name the three ways to...

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