Geometry – Review for First Semester Final

Unit 1

Use the diagram to answer the questions.

1. Are N, R, and C collinear? _______

2. Are N and J collinear? _______

3. Are J, R, and C collinear? _______

4. Are N, R, and C coplanar? _______

5. Are J, R, and F coplanar? _______

6. Are J, R, F, and G coplanar? _______

7. Are N, R, C, and J coplanar? _______

8. Are N, R, C, and G coplanar? _______

9. Are N, R, J, and G coplanar? _______

10. Are and parallel, intersecting or skew? _________________________

11. Are and parallel, intersecting or skew? _________________________

12. Are and parallel, intersecting or skew? __________________________

13. Where does intersect ? _______

14. Where does plane NRJ intersect plane JGF? _________________

15. Two points are collinear __________________ (sometimes, always, or never)

16. Three points are collinear _________________ (sometimes, always, or never)

17. Three points are coplanar _________________ (sometimes, always, or never)

18. Four points are coplanar __________________(sometimes, always, or never)

19. Point S is between R and T on . Use the given information to draw a clearly labeled diagram and

write an equation in terms of x. If RS = 3x – 7, ST = 5x + 8, and RT = 73, find x and ST.

20. Point J is the midpoint of N and H on a line segment. If NJ = 6x + 3 and NH = 8x + 18,

find x and the length of .

N

R

C

J G

F

Name _________________________________

Date _________________ Per ______

Invisiblelines

Y countyNONO 7 Any3 pointsy that makea

y3eoffinetanrem have tobe

N11Skewintersecting

pointR sJRalwayssometimesalwayssometimes

X 9ST 53

X 3NH 42

21. Find the area and perimeter of the triangle. 22. Find the area and perimeter of the triangle.

23. Find the area and perimeter of the triangle. 24. Find the area and perimeter of the triangle.

25. If a line passes through (-8, 7) and (12, 2), find . . .

a. The slope of the line. b. The equation of the line. c. The midpoint of the points.

d. The distance between the e. The equation of a line parallel d. The equation of the line points. to the line that passes through perpendicular to the line (16, 20). that passes through (16, 20).

x y

4

8

9

10 x

3 7

y

6

2

-2 -6

y

x

C D

G

6

2

-2 -6

y

x

F N

T

Tito yy10.4 141

A _52 A 3510 33.9 10 31.5

A_28 A 20p 24.5 10 22.4

yaYi 7 28 12

520XzXit4

m 4 y 4 5 2 E

20.6 9 4 124 y 4x 44

26. Find x and justify. 27. Find and justify. 28. Find and justify.

29. Find x and justify. Draw a well labeled picture and write a segment addition statement for each of the following. Then solve.

30. ∠ is complimentary to ∠ . 31. ∠ is supplementary to ∠ . If m∠ 11 8 ° If m∠ 9 22 ° and m∠ 8 6 ° and m∠ 2 18 ° find x and m∠ find x and m∠

L

D

B M

(10x + 18)° (4x – 6 )°

H

F

O

X (6x – 8)°

(2x+ 5)°

(10x – 21)q P

R

T A (3x + 3)°

(14x + 2)°

G

K

T

R

a

6 81 2 5 10 21

11 9 AngleAddition 4 5 Complimentary K12 Linearpairpost

11 8 DefofL X 4 Complimentary 4 20 LinearBisector pair

Unit 2 Fill in the table for: A right triangle has one 90°angle.

Statement Type Statement Truth Value

Negation

Conditional Converse

Biconditional

Inverse

Contrapositive Name the Property that justifies each statement. 1. If TR VB, then VB TR _____________________________________________________________

2. If ≅ and ≅ , then ≅ __________________________________________________________

3. If GH JY, then GH – 5 JY –5 ___________________________________________________________________________

4. ≅ ____________________________________________________________________________________________________

5. If m∠W m∠X and m∠X m∠C, then m∠W m∠C___________________________________________________

6. If m∠P m∠A, then m∠A m∠P __________________________________________________________________________

7. FG GF_______________________________________________________________________________________________________

8. If ∠Z ≅ ∠R, then ∠R ≅ ∠Z___________________________________________________________________________________

9. If m∠V 9 and m∠L 9, then m∠V m∠L ____________________________________________________________

10. If ≅ , then ≅ ________________________________________________________________________________

11. If TN RC, then TN FX RC FX ______________________________________________________________________

12. ∠S ≅ ∠S ____________________________________________________________________________

13. If CB 14 and MX 14, then CB MX ____________________________________________________________________

14. If x 3 22, then x 19 ___________________________________________________________________________________

15. If ∠R ≅ ∠G and ∠G ≅ ∠Y, then ∠R ≅ ∠Y. _________________________________________________________________

SymmetricTransitive po E

subtractionPOEReflexive DO

Transitivesymmetric DOE

Reflexive POEsymmetric Po

Transitive DOEsymmetric PoAddition POE

Reflexive PoTransitive POE

subtraction poETransitive Poc

Complete each statement according the property given.

16. Symmetric Property of Equality: 22. Transitive Property of Congruence:

If m∠B m∠V, then _______________________ If ∠E ≅ ∠M, and ∠M ≅ ∠W, then ____________

17. Addition Property of Equality: 23. Symmetric Property of Congruence:

If NT RF, then NT AC ______________ If ≅ , then ___________________

18. Transitive Property of Equality: 24. Reflexive Property of Congruence:

If PB JA and JA YK, then _______________ ≅ ________________

19. Reflexive Property of Equality: 25. Symmetric Property of Congruence:

m∠F ______________ If ∠P ≅ ∠C, then __________________

20. Multiplication Property of Equality: 26. Reflexive Property of Congruence:

If AW VT, then 8 AW _______________ ∠Y ≅ ________________

21. Subtraction Property of Equality: 27. Transitive Property of Congruence:

If m∠K m∠R, then m∠K – m∠A ____________ If ≅ and ≅ , then ______________

Solve for x and justify.

28. 29. 30.

(5x + 10)q (7x – 12)q

(9x)q

(6x + 36)q

(3x + 12)q

(7x + 18)q

M LV _MLB LEELW

RFTAC EM EIR

pB Yk GT3 or 136

MLF CELP

shut cyMCR MCA DT FQ

x41 vertical is 4 12 vertical's Xuslinearpair

Unit 3

Solve for x and justify.

1. 2. 3.

4. Graph y –3x 5 5. Graph y 4x – 3 6. Graph y – x 4

7. Find the shortest distance from the 8. Find the perimeter and area of the triangle point to the line. enclosed by the three lines. y = x – 1 y = 4 x = -2

(10x – 5)°

(7x + 37)° (6x)°

(4x + 18)°

(3x + 10)°

(8x – 50)°

A

7 137 10 5

4 14 Corresponding X 9 Art Intl's 420 LinearPairL'spost

or a or

o s

o

v v

Iz I 23M 123 13,7

FEDcspthof aFoo eTiz o

a

c213 A24.511.2 p 23.9

Unit 4

Perform each of the following transformations.

(* Assume all rotations are counter-clockwise and don’t forget to label the image using prime marks.

1. A reflection in the 2. A translation for 3. A rotation of 90° 4. A reflection in the the y - axis (x, y) → (x + 4, y – 1) about the origin. line y = -2 5. A translation for 6. A rotation of 270° 7. A reflection in the 8. A rotation of 180° (x, y) → (x – 6, y ) about the origin. line y = –x about the origin. 9. A translation for 10. A reflection in the 11. A rotation of 90° 12. A translation for (x, y) → (x + 6, y) line x = -1 about the origin. (x, y) → (x – 3, y + 5) 13. A rotation of 270° 14. A reflection in the 15. A translation for 16. A reflection in the about the origin. line y = x – 1 (x, y) → (x + 6, y – 2) line y = –x + 1

G

R N

H

P W E B

A

R C

X

V

O

Z M U

D

C

R

A J

O

G

E

N T

S

R W

P

D V

F

U R

A P

T

L

O

G

M

D

C

L N

Y

G 1.3µHP p sE

pi p c oops

v i

c omi oo iA p CDU

i n EDI s sl v p u oop

e l siI

oop iN w R

Right down2 Po

po yni i iD

P i

g om

17. If a triangle with vertices at A(–2, 6), B(8, 5), and C(12, –10) were translated according to the rule (x, y) →(x – 6, y + 9), where would the coordinates of the image be located? 18. Rotate the image 240° counter-clockwise. 19. Find the number lines of reflectional symmetry

and the degree of rotational symmetry.

20. 21. Graph triangle TKM with vertices

a. Find m∠KXR _________ T(-5, 2), K(6, 3), and M(2, -4)

and its image after a dilation

b. Find m∠FXY _________ with a scale factor of 2.

c. Name the image of C for a rotation of 72° about X.

d. Name the image of G for a rotation of 108° about X.

e. Name the image of Y for a rotation of 288° about X.

f. Name the image of K for a rotation of 216° about X.

g. How many degrees would point B need to rotate to

rest in the same position as point S?

A

B

C

K

G

B C N

R

Y F O S

X

y

x

AY8,15JB 2,14c 6517

9A

400

pp

36,01 36

36 µ108

36635 9

K

NO

G

2520f yo y ki 12,6JM't458

Unit 5 1. Find x and justify. 2. Find x and justify. 3. Find x and justify.

4. For each of the problems below, determine if there is enough information to say that the triangles are congruent and if so finish the a triangle congruence statement and justify your reasoning. If not write “not enough information.” a. b. c. d. e. f. 5. If ∆NFT ≅ ∆KMP, find x and y. Then find the measure of every angle. Show your work.

(3x + 9)°

(2y + 17)°

N

F

T

(2x + 28)°

(4y – 25)°

P

K

M

(6x – 2)°

3x°

40°

48°

(9x + 2) °

(20x – 6)° 4x°

48°

K B

Y W

M H

J P

G P

Y Z

T N

S F

R E

D X

R C

D V

x = y =

m� =

m� =

m� =

m� =

m� =

m� =

1110.5 A Sumth 4 5.1 ext L th X44 Sext L th

otions

q

19 21e u 66 6659 59Ss 55

3 9 2 28 fZyth Uy 25

6. If ∆HFT ≅ ∆DRP, if m� = 24q, and m� = 83q, then m� = __________. 7. A triangle has angle measures such that the measure of angle A is seven less than angle C, and the measure of angle B is two more than three times angle C. Find the measures of the angles. (Hint: Draw a picture.) Show your work.

8. R(-3, 8), S(2, -4), T(6, 2) 9. Given: ∠ ≅ ∠ , and is the midpoint of

My hypothesis is that the triangle is a Prove: ∆TCN≅ ∆RPN

______________________________.

10. Given: // , and ≅

Prove: ∆RXE ≅ ∆DEX

R

P

T

Side Length Slope

Conclusion:

_____________________________________

_____________________________________

_____________________________________

m� =

m� =

m� =

R E

D X

73

1133037

Gwendef ofmidpointvertical LlsASAs post

IT 10 8 ZzEs 13 1215IT 7.2 312

GivenGivenA It int L'sReflexive PocSAS S E post

7. Given: ∠MTP ≅ ∠MRW, and ≅ Prove: ∠W ≅ ∠P

T

M

W P

R

(Hint: It may help to trace one triangle with a highlighter, and trace the other triangle with a different color highlighter.)