geometry/trig 2name: __________________________ unit 3 review packet – page 2 – answer keydate:...

Geometry/Trig 2 Name: __________________________

Unit 3 Review Packet – Page 2 – Answer Key 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 c || d

2.) m1 = m4 None

3.) m12 + m14 = 180 a || b

4.) m1 = m13 None

5.) m7 = m14 c || d

6.) m13 = m11 None

7.) m15 + m16 = 180 None

8.) m4 = m5 a || b

c d

Section II - Proofs

Statements Reasons

J

G K

IH

1. Given: GK bisects JGI; m3 = m2

Prove: GK || HI

1. GK bisects JGI

2. m1 = m2

3. m3 = m2

4. m1 = m3; 1 3

5. GK || HI

1. Given

2. Definition of an Angles Bisector

3. Given

4. Substitution

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

2

1

3

Geometry/Trig 2 Unit 3 Proofs Review – Answer Key

Statements Reasons

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

1 2 3

4

5

A C

D

EF

B

J K

1. AJ || CK 1. Given

2. m1 = m3 2. If two parallel lines are 1 3 cut by a transversal, then

corresponding angles are congruent.

3. m1 = m5 3. Given

4. m3 = m5 4. Substitution 3 5

5. BD || FE 5. If two lines are cut by a transversal and corresponding angles are

congruent, then the lines are parallel.

Statements Reasons

S T

P

RQ

3. Given: ST || QR; 1 3 Prove: 2 3

1 3

2

1. ST || QR 1. Given

2. 1 2 2. If two parallel lines are cut by a transversal, then corresponding angles are congruent.

3. 1 3 3. Given

4. 2 3 4. Substitution

Statements Reasons

4. Given: a || b; 3 4 Prove: 10 1 1

3 4

5

6

7 8

910

2

b

a

c d

1 3

54

6 7

28a

b5. Given: a || b

Prove: 1 and 7 are supplementary.

Statements Reasons

1. 3 4 1. Given

2. 1 3 2. Vertical Angles Theorem


4. a || b 4. Given

5. 4 7 5. If lines are parallel, then alternate interior angles are congruent.


7. 7 10 7. Vertical Angles Theorem


1. a || b 1. Given

2. m1 + m4 = 180 2. Definition of Linear Pair/Angle Addition Postulate

3. m4 = m7; 4 7 3. If lines are parallel, then alternate interior angles are congruent.

4. m1 + m7 = 180 4. Substitution

5. 1 and 7 are supplementary 5. Definition of supplementary angles


Unit 3 Review Packet – Page 5 – Answer Key Date: ___________________________

Statements Reasons

6. Given: BE bisects DBA; 1 3 Prove: CD // BE

C

D EA

B

32

1

1. BE bisects DBA 1. Given

2. 2 3 2. Definition of an Angle Bisector

3. 1 3 3. Given


5. CD // BE 5. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

7.

Statements ReasonsGiven: AB // CD; BC // DE

Prove: 2 6

AC E

DB


Unit 3 Review Packet – page 6 – Answer Key Date: ___________________________

2

1 3 4 5 7

6

8.Statements Reasons

A

DB

2

1 3 4 5 7

6

C E

Given: AB // CD; 2 6

Prove: BC // DE

1. AB // CD 1. Given

2. 2 4 2. If two parallel lines are cut by a transversal, then alternateinterior angles are congruent.

3. BC // DE 3. Given



1. AB // CD 1. Given


3. 2 6 5. Given


5. BC // DE 3. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Section VI – Solve each Algebra Connection Problem.

1. 2.

4.3.

75

30

5x

x = 21

y = 75

w = 37

x = 143

y = 71.5

z = 86

x = 30

y = 5

37 2y

z + 57

w

x

4x - 5 23y

65 125

y

x + 12

6x 8x + 1

x = 11

6.5.4x + 13 4x + 25

6x6x

4x + 25 4x + 13

x = 23

A B

CD

x = 20

Is AB // DC? yes

Is AD // BC? no

80

5x 4x + 17

83


Unit 3 Review Packet – page 7– Answer Key Date: ___________________________


Unit 3 Review Packet – page 8 – Answer Key Date: ___________________________

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 Triangle 180 60 360 120 0

4 Quadrilateral

360 90 360 90 2

5 Pentagon 540 108 360 72 5

6 Hexagon 720 120 360 60 9

7 Heptagon OR

Septagon

900 128.57 360 51.43 14

8 Octagon 1080 135 360 45 20

9 Nonagon 1260 140 360 40 27

10 Decagon 1440 144 360 36 35

n n-gon 360180)2n(

n180)2n(

n360

2)3n(n

geometry/trig 2name: __________________________ unit 3 review packet – page 2 – answer keydate:...

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