Name: __________________________________________ Date: _____________________ Per: ____

Geometry Semester 1 Final Exam Review

Chapter 1: Tools of Geometry

1) Find a pattern for the sequence. Use the pattern to show the next three terms. 15, 12, 9, 6, …

2) If two lines intersect, then they intersect in a ___________________.

3) If two planes intersect, then they intersect in a __________________.

4) Which of the following could not be the intersection of two planes?

a. AB b. BA c. B d. ABC e. point A

5) B is the midpoint of AC . If 2 1AB x and 3 4BC x , what is x? What is the measure of BC ? What is

the measure of AC ?

6) Find the midpoint and distance on a number line between 6 and -15.

7) S is between R and T. If 64, 3 1RT RS x and 2 2ST x , find x.

8) Draw an example of each of the following

a. Complementary b. Supplementary c. Vertical angles d. Adjacent

Angles angles angles

9) 2 8, 3 14, 7 2m RST x m TSW x m RSW x . Find m TSW .

10) Find .m RQS

2 4x 6 20x

T Q R

S

11) Find the measure of x.

3 31x 2 6x

12) Find TO given

2 12

5

50

TO x

OP x

TP

13) What is the measure of this angle?

How would you classify the angle?

14) EM bisects GEO

3 5

29

m GEM x

m MEO x

Find m GEO .

15) 2 15m GIT x

4 5

m FIT x

m GIF x

Find m GIT .

16) Given the points 2, 4 and 5,1 :

a. Find the distance between the points.

b. Find the midpoint between the points.

17) Given the points 6, 5 and 3,2 :

a. Find the distance between the points to the nearest tenth.

b. Find the midpoint between the points.

18) O is the midpoint of DG . Find the coordinate of G if O is 7 and D is 3.

T O P

G

T I

F

19) Which is the missing endpoint if the midpoint is 0, 6 and the other endpoint is 3,8 ?

a. (1.5, 1) b. (1, 1.5) c. (-3, -20) d. (20,-3)

20) I. What is the circumference of a circle with: (Leave answers in form)

a. Radius of 4 cm b. diameter of 32 cm

II. What is the area of a circle with: (Leave answers in form)

b. Radius of 4 cm b. diameter of 32 cm

21) The perimeter of a rectangle is 28 feet and the base is 8 feet. What is the height?

22) The area of a rectangle is 254 cm and the height is 9 cm. What is the base?

Chapter 2: Reasoning and Proof

23) Given the sentence “If you are good, then Santa will bring you presents,” write:

a. The converse:

b. The inverse:

c. The contrapositive:

d. The biconditional:

24) Draw a conclusion:

-If a student gets an A on the final exam, then the student will pass the course.

-Felicia gets an A on the music theory final exam.

25) Draw a conclusion:

-If it is a national holiday, then school is not in session.

-If school is not in session, then students are at home.

26) Which property of equality or congruence justifies each statement?

a. If 3 14 80x , then 3 66x .

b. If 15m A , then 3 45m A .

c. If 4 100m C , then 25m C .

27) Solve for y.

28) Solve for x.

29) ABC and DBC are complementary. What is the m DBC if 4 10m ABC x and 30m DBC x ?

30) If the supplement of T is 47 , what is the measure of T ?

Chapter 3: Parallel and Perpendicular Lines

31) Determine the relationship of the following angles.

a. 1 and 2

b. 1 and 6

c. 3 and 6

d. 1 and 7

e. 1 and 5

f. 2 and 4

32) Fill in the blank.

a. Angles that form a linear pair ___________________________.

b. Angles that are vertical are _____________________________.

c. Corresponding angles of parallel lines are _______________________________.

d. Same-side interior angles of parallel lines are ______________________________.

4 3 2 1

5 6

7 8

e. Alternate interior angles of parallel lines are _______________________________.

33) If 50, 130, 50m A m B m C , and they fall on parallel lines cut by a transversal

a. Which angles could be vertical?

b. Which angles could be same-side interior?

c. Which angles could be alternate interior?

34) In FUN , the angles measure 3 , 2 20 , 5 5x x and x , what is the measure of the smallest angle?

35) What is ?m DBA

36) What is the value of x?

37) What is the value of x?

38) If 60m A and 60m B , ABC is what kind of triangle? Classify by angles and sides.

39) If 45m A and 45m B , ABC is what kind of triangle? Classify by angles and sides.

40) Classify the triangle according to the angle and side length.

B C A

D

x

x 63

36

41) Find the missing angle measure.

a. b.

42) Find the sum of the measures of each polygon.

a. Dodecagon b. nonagon

43) Find the measure of an interior angle and an exterior angle of each regular polygon.

a. Pentagon b. 18-gon

44) Find the slope of the line passing through the following points:

a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8)

45) Find the slope of the line parallel to the line passing through the following points:

a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8)

46) Find the slope of the line perpendicular to the line passing through the following points:

a. (-2, 3) and (-6, -5) b. (6,9) and (-3, -8)

47) Determine which line is perpendicular to 2

63

y x .

a. 2

73

y x

b. 3

52

y x c. 3

82

y x

d. 2

63

y x

48) Determine which line is parallel to 4 3y x .

a. 1

74

y x

b. 1

54

y x c. 4 8y x d. 4 6y x

49) How can you determine if two lines are parallel?

50) How can you determine if two lines are perpendicular?

51) How can you determine if two lines intersect, but are not perpendicular?

52) Given AD BC , find m BDA

53) Given: l m , find x.

Chapter 4: Congruent Triangles

54) Given that IMP OGR , name all of the pairs of corresponding parts.

55) For each figure below, state the parts you would need to know are congruent in order to prove the triangles

congruent by the method stated.

a. SAS b. AAS

C T

c. HL d. ASA

56) Use the given information to make a conclusion about each figure.

a. I) Y is the midpoint of RD

II) UY RD

A B

C D

B

T

I

D

M A

M T

S

R

D U

P M

D

C

A

T

O

G

R

U

Y D

III) UY bisects RUD

b.

I) DA QU

II) What parts are congruent just by the picture?

57) Given: JOA ADJ

ON ND

Prove: JON ADN

58) Given: T is the midpoint of GF

GTI FTI

Prove: G F

59) Given: SL CL

SA AU

SC SU

SLA is isosceles with base LA

Prove: SCL SUA

J

O N

A

D

R

I

G F T

D A

Q U

S U

A

L C

60) A is the midpoint of LU

2 14

3 24

10

CAL x

SAU x

CA x

Find the measure of SA .

61) Find x

62) TAP is isosceles with vertex angle t.

Find m A .

63) DAN is isosceles with base AD .

4 12

33

A x

D x

Find m D

64) ABC is isosceles with A as the vertex angle. If 3 4, 5 8m B x m C x . Find m B

Chapter 5: Relationships within Triangles

C

L A

S

U

x

P

T

A

D A

N

65) In ,MLK MK is 20in. long. What is its midsegment?

66) Solve for x.

67) Solve for y.

68) a. If 24, 6, 8DF BC and DB ,

what is the perimeter of EBC ?

b. If the perimeter of BCE is 17,

what is the perimeter of ADF ?

69) LJ bisects KLM , find x, JK, and JM.

70) AB is a median. CD = 18, BD = x-6. Solve for x.

84

D

B C

A E F

J

K

L M

B

A

D C

71) G is the centroid

a. If GD = 7, what is AG?

b. If GC = 12, what is CF?

c. If EB = 48, what is GB?

72) In , 10 , 16 , 14FUN UN cm UF cm and FN cm . Which angle is the smallest?

73) In , 47, 93HAT A T . List the sides in order from least to greatest.

74) Could the following be lengths of a triangle?

a. 5, 9, 13

b. 7, 14, 20

c. 1, 5, 7

d. 2, 2, 3

75) If one side of a triangle is 17 cm and the second side is 39 cm, what are the possible side lengths for the third

side?

Geometry Semester II Review Packet #1

A

E

C

D F

B

G

8.1 Ratio and Proportion Ratio = Proportion = Solve proportions by cross multiplying. extremes means

a c

b d

word problems – set up what is being compared

8.1

1. 3 9

4 12 Name the means.

2. Is 7

8

x

y equivalent to

7

8

x

y?

3. Solve. 11

5 35

x

4. Solve.

2 5

8

x

x

5. The angles of a triangle are in the ratios

3:5:7. Find each angle measure.

6. If 2 CDs cost $14.50, how much will 15

CDs cost?

7. A 15 foot building has a 9 foot shadow.

How tall is a building with a 30 foot

shadow?

8.2 Similar Polygons Similar polygons:

1) Corresponding angles are congruent. 2) Corresponding sides have equal ratios.

Scale factor = ratio of sides

8.2

8. What is the scale factor of ABCD to

EFGH?

9. Find EF, FG, and GH.

10. Find x and y.

D

A

C

B

12

25

8

20

E F

G

H

6

ABCD ~ EFGH

18 30

24

20

x

y

8.3 Similar Triangles Ways to prove similar triangles:

1) SSS~ 2) SAS~ 3) AA~

8.3

11. Are these triangles similar? Why?

12. Are these triangles similar? Why?

13. ABC DEF

15

20

25

16

AB

AC

BC

DF

8.4 Proportional Parts Side-splitter

a c

b d

Midsegment:

1) ½ the 3rd side 2) Parallel to the 3rd side

a c

b d

8.4

14. Find x and y.

15. Find x.

16. Find x and y.

12

8

9

6

Find EF

Find DE

15

24

y

10

x

52

4

x

a

b d

c

a

b d

c

2

3 x

8

5 y

8.5 Parts of Similar Triangles In similar triangles, the ratio of the sides is also the ratio of the:

Perimeters

Medians

Altitudes

Angle bisectors

8.5

17. Find x and perimeter.

~

18. Find x.

8 10

P = 28

6 x

P = ?

9 6

x 8

Answers:

1) 3, 0, -3

2) Point

3) Line

4) C, D, E

5) X = 5, 11, 22BC AC

6) Midpoint: -4.5, Distance: 21

7) X = 13

8) A)

B)

C)

D)

9) X = 12, 50m TSW

10) X = 19.5, 137m RQS

11) X = 31

12) X = 11, 34TO

13)

14) X = 12, 82m GEO

15) X = 10, 35m GIT

16) A) 74 8.60

B) 3 3

,2 2

17) A) 130 11.4

B) 3 3

,2 2

18) 11

19) C

20) IA) 8 cm IB) 32 cm

IIA) 216 cm IIB) 2256 cm

21) h = 6 ft

22) b = 6 cm

23) a) If Santa brings you presents, then you

were good

b) If you are not good, then Santa will

not bring you presents

c) If Santa does not bring you presents,

then you were not good

d) Santa will bring you presents if and

only if you are good

24) Felicia will pass the course

25) If it is a national holiday, then students are

at home

26) a) Subtraction property of equality

b) Multiplication property of equality

c) Division property of equality

d) Symmetric property of congruence

27) y = 18

28) x = 6

1 2

29) x = 14, 44m DBC

30) 133m T

31) a) Supplementary angles

b) Alternate interior angles

c) Corresponding angles

d) Corresponding angles

e) Same-side interior angles

f) Vertical angles

32) a) are supplementary

b) Congruent

c) Congruent

d) Supplementary

e) Congruent

33) a) ,A C

b) , , ,A B and C B

c) ,A C

34) x = 15,5, smallest angle = 46.5

35) 110m DBA

36) 70x

37) x = 50

38) Equiangular and equilateral

39) Right and isosceles

40) Acute and scalene

41) a) 102y

b) n = 113, n+6=119

42) a) 1800 b) 1260

43) a) interior = 108, exterior = 72

b) interior = 160, exterior = 20

44) a) m = 2 b) 17

9m

45) a) m = 2 b) 17

9m

46) a) 1

2m

b)

9

17m

47) C

48) D

49) If the slopes are the same

50) If the slope are opposite reciprocals

51) The slopes are different by not opposite

reciprocals

52) 40m BDA

53) x = 20

54) , ,I O M G P R

, ,IM OG MP GR IP OR

55) A) BI MD

B) T G

C) RM RS

D) MUP DPU

56) AI) RY YD

AII) 90m UYD m UYR

AIII) RUY DUY

BI) DAQ UQA

BII) QA QA reflexive property

57) Statement Reason

JOA ADJ Given

ON ND Given

ONJ DNA Vertical angles

JON ADN ASA

58) Statement Reason

T is the midpoint of GF Given

GTI FTI Given

TI TI Reflexive

GTI FTI SAS

G F CPCTC

59) Statement Reason

SL CL Given

SA AU Given

SC SU Given

SLA is isosceles Given

CLS and UAS Definition perpendicular

are right angles lines

CLS UAS All rt. Angles are

congruent

SCL SUA HL

60) x = 38, SA = 28

61) x – 80

62) 62.5m A

63) x = 15, 48m D

64) x = 6, 22m B

65) 10 in

66) x = 23

67) y = 7

68) a) 52 units b) 34 units

69) x = 12, JK = 17, JM = 17

70) x = 15

71) a) 14 b) 18 c) 16

72) F

73) , ,AT HT AH

74) a) yes b) yes

c) no d) yes

75) 22 56x

8.1

1) 4 & 9

2) 3 & 12

3) no

4) 16/3

5) 12

6) 108.75

7) 50 ft

8) 4:3

9) EF =15

FG = 9

GH = 75/4

10) x = 16, y=12

8.3

11) yes, SAS~

12) yes, AA

13) EF = 20, DE = 12

8.4

14) x = 16, y = 20

15) x = 8

16) x = 12, y = 20

8.5

17) x = 7.5, P = 21

18) x = 12