Geometry Name: _______________________ Chapter 3 Review Sheet Period: Group#:_____ Hmwk #9 1. Describe the following segments or planes as intersecting, parallel, or skew. a. AB and

DE ___________________________

b. AB andHC ___________________________ c. AF and CH ___________________________ d. planes ABC and DEH ___________________________ 2. Given the diagram, identify the transversal and classify each pair of angles as corresponding, alternate

interior, alternate exterior, or consecutive interior angles, vertical angles, and linear pairs.

Transversal Angle Relationship a. ! 1 and ! 5 ___________________ b. ! 15 and ! 16 ___________________ c. ! 7 and ! 5 ___________________ d. ! 10 and ! 14 ___________________ e. ! 8 and ! 9 ___________________

3. Given

a ! b , find the m!1 Be sure to provide a brief explanation for each equation.

a. b. c.

�

x2! 5x

�

!6x + 56

1 a

b

2 8 7

1

9 10 11 12 13 14 15 16

3 4 6

5

a c

d

b

H

CB

G

A

F

D

E

1

5x - 10

8x - 5

b

a 1

4x + 57

7x - 3

b

a

4. Determine whether

a ! b . Then briefly justify, in complete sentences why

a ! b or why a and b are not

parallel. Be sure to provide a a brief explanation for each equation. a) b) 5. Given

s ! r , m!5 = 115 and m!8 = 45 , find the measure of all the angles.

a)m!1 = ____________ b) m!2 = ____________ c) m!3 = ____________ d) m!4 = ____________ e) m!6 = ____________ f) m!7 = ____________ g) m!9 = ____________ h) m!10 = ____________ i) m!11 = ____________ j) m!12 = ____________ k) m!13 = ____________ l) m!14 = ____________ m)m!15 = ____________ n) m!16 = ____________ 6. Given the diagram withm!1 = 48 , find all the missing numbered angles.

m!1 = 48 a) m!2 = ________ b) m!3 = ________ c) m!4 = ________ d) m!5 = ________ e) m!6 = ________ f) m!7 = ________ g) m!8 = ________ h) m!9 = ________ i) m!10 = ________

s r

1

2

3

4

5

6

7

8

9

10 11

13

12

14

15

16

a

b

a

b

(2x + 5)°

(3x-10)° (2x+20)°

a

b (3x + 12)°

(x2 + 7x)°

(5x+8)°

10

98

7

6

5

43

21

7. Find the value(s) of x of the measure of!1. Be sure to provide a brief explanation for your equation. 8. Find the value of x and y. Be sure to provide a brief explanation for your equation.

9. a. Sketch a line with a slope of! 12

passing through (0, -4).

b. Find the slope of the line through (0, 7) and (-3, 9). c. What is the slope of a line parallel to the line in part b? d. What is the slope of a line perpendicular to the line in part b? e. Find R so that the slope of a line through (2, R) and (8, 4) is 3.

1

�

3x2

�

24 + 6x

4x

x + 2y

2x + y

10. Write the equation of the line with a slope of 12

and through the point (2, 5).

11. Write the equation of the line parallel to y = 3x + 5 and containing the point (-1, 4). 12. Write the equation of the line perpendicular to 2x + 6y = 7 and containing the point (3, 1). 13. Write the equation of a line perpendicular to AB

! "##, give A (5, 1) and B (-3, -2) and containing point B.

14. Write the equation of the line from C perpendicular toAB (called the altitude).

A(-3, 2) B(6, 3)

C(-1, 8)

Y

X

Complete the following proofs. 15. Given: !1 " !3 !2 " !4 Prove:

DE ! AB

16. Given:

g ! h

h ! j

Prove: !1 " !3

E

D

C B

A

3

2

1

4

g

h

j

1

2

3

BONUS QUESTION (+1) Given

a ! b ! DG and

CD ! EF andm!1 = 62, find the measure of all the angles.

a)m!2 = ____________ b)m!3 = ____________ c)m!4 = ____________ d)m!5 = ____________ e)m!6 = ____________ f)m!7 = ____________ g)m!8 = ____________ h)m!9 = ____________ i)m!10 = ____________ j)m!11 = ____________ k)m!12 = ___________ l)m!13 = ____________ m)m!14 = ____________ n)m!15 = ____________ o)m!16 = ____________ Answers: 1a. parallel b. parallel c. skew d. intersecting 2a. c, alternating exterior b. none, linear pair c. c, corresponding d. d, alternate interior e. a, consectutive interior 3a. x = -8 & 7, m!1 = 166!or !76 b. x = 15, m!1 = 115 c. x = 20, m!1 = 43 4a. no the line are NOT parallel b/c the alt ext are not cogruent proving the lines are NOT parallel b. yes the lines are parallel b/c the corresponding angles (or alt int angles) are congruent proving the lines are parallel 5a. 65 b. 115 c. 45 d. 135 e. 65 f. 45 g. 65 h. 65 i. 115 j. 135 k. 45 l. 115 m. 135 n. 135 6a. 132 b. 132 c. 48 d. 48 e. 42 f. 42 g. 138 h. 138 i. 42 7. x = 4 & -2, m!1 = 132!or !168

8. x = 20, y = 40 9b. !2

3 c. !

2

3 d. 3

2 e. R = -14 10. y =

1

2x + 4 11. y = 3x + 7 12. y = 3x ! 8 13. y = !

8

3x !10

14. y = !9x !1 15. state given, state vertical angles, state substitution, state angle relationship, state why lines are parallel 16. state given and angle pair relationship, state other given and angle pair relationship, state substitution, state why angles are

congruent

GF

E

D

C

b

a

16

15

14

1312

1110

9 8 7

6 5

4321