ALLEN PARK HIGH SCHOOL

Geometry First Semester Review Winter 2010

APHS/MATH

ALLEN PARK HIGH SCHOOL F i r s t S e m e s t e r R e v i e w

GEOMETRY

Winter 2010


APHS/MATH 1 GO ON TO THE NEXT PAGE

DIRECTIONS This section of test is 68 items, which you will work in this booklet. Mark the correct answer as directed by your teacher. You may use a calculator that has been approved by your teacher. Only your test booklet and calculator may be used; no other materials should be on your desk. 1 The statement, “4 is an even number, and all even numbers are divisible by 2; therefore, 4 is

divisible by 2”, is a form of ________________ reasoning.

For questions 2-4, use the following statement.

“If there is a lot of snow on the ground, it must be cold.”

2 State the Converse on the conditional statement. 3 State the Inverse of the conditional statement. 4 State the Contrapositive of the conditional statement. 5 The table below shows the truth values for statements p and q. Complete the third column for

the truth value of the statement “p or not q,” symbolized ~p q . Circle the correct answer.

p q ~p q

T T

T F

F T

F F

A. F B. F C. T D. T T T T T T F F F F F T F



26

2524

23

2221

20191817

1615

14

1312

1110

98

7

65

43

21

105

65

qp

l

m

n

6 The table below shows the truth values for statements p and q. Complete the third column for the truth value of the statement “q and not p,” symbolized q p .

p q q p

T T

T F

F T

F F

7 Given the statement, “If it is icy outside, then the roads are slippery.” Find a statement which

would be considered logically equivalent. Use the figure below to answer questions 9 – 15 given that lines n, m, and l are parallel. 8 Find all of the remaining angles. 9 What is the relationship for 15 and 19 ?

10 What is the relationship for 2 and 10 ?


12 What is the relationship for 12 and 14 ? 13 What is the relationship for 7 and 8 ?


15 If 22 (7 15)m x and 17 25m , find x.

16 Define the following:

Point – Line – Plane – Angle – Ray – Postulate – Theorem – Corollary -



YXW

GFD

9y - 452y + 5

3x7x + 20

Z

Y

X

W

17 The proof of a geometric situation is shown below. Fill in the remaining.

Given: , DF WX FG XY

Prove: DG WY Statement Reasons

1. , DF WX FG XY 1. Given

2. ,DF WX FG XY 2. Definition of __________________

3. ________, WY _________DG 3. Segment Addition Postulate

4. ________DG 4. Substitution Property

5. DG WY 5. ?

6. DG WY 6. Definition of congruent segments 18 The diagram below shows two mitre cuts of baseboards for a floor. The measures of the

angles formed are shown in the diagram, in terms of x and y. Find the value of x and y.

19 In the figure below, XYZ measures 80 , YZX measures 55 , and points W, X, and Y are

collinear. What is the measure ofWXZ ?



6 ft

3 ft

Z

Y

X

W

Use the figure to answer questions 20 – 24. 20 What is the perimeter of the rectangle represented by the drawing above? 21 What is the area of the rectangle represented by the drawing above? 22 What is the area of the triangle represented by the drawing above? 23 What is the relationship between the area of the rectangle and area of the triangle? 24 What is the length of the diagonal in the rectangle represented by the drawing above? 25 In the figure below, XYZ measures 80 , YZX measures 55 , and points W, X, and Y are

collinear. What is the measure ofWXZ ?



X

W

V

U

T

S

R

170

160

150

140

130

120

110

80

30

20

10

40

50

60

100

70

90

100

80

70

110

120

60

50

130

40

140

30

150

20160

17010

26 Using the protractor above, find the measure of RXU .

27 Using the protractor above, find the measure of WXT . 28 Using the protractor above, find the measure of RXS . 29 Using the protractor above, find the measure of TXV . 30 Using the protractor above, find the measure of UXV .

31 In the standard ,x y coordinate plane, a line segment has its endpoints at 7,12 and 13,4 .

What are the coordinates of the midpoint of the line segment?

32 In the standard ,x y coordinate plane, a line segment has an endpoint at 2,5 and a midpoint

at 7,10 . What are the coordinates of the other endpoint of the line segment?



M

L

KJ

33 In the standard ,x y coordinate plane, a line segment has an endpoint at 3,5 and another

endpoint at 5,4 . Determine the length of the segment?

34 While constructing a center drain for a circular pool, the length of pipe needed to be dug out is 13 feet. Using 3.14 for , what is the approximate area, in square feet, of the bottom of the

pool? 35 The proof of a geometric situation is shown below.

Given: JLM is isosceles.

MK bisects JL .

Prove: LJ

Statement Reasons

1. JLM is isosceles, MK bisects JL 1. Given

2. JM LM 2. Definition of ____________

3. JK LK 3. Definition of ____________ 4. ? 4. Reflexive 5. JKM LKM 5. ?

6. ? 6. ? 36 If one leg of a right triangle is 10 inches long, and the hypotenuse is 14 inches long, how many

inches long is the triangle’s other leg?

37 The three angles of a triangle are 2 , 5 20, and 48x x x . Find x and the largest angle.



Q

P

N

M

38 A builder has a wooden board measuring 224 inches long. He needs to cut this board to make 12 plaques. What should the length of each plaque be?

39 The coordinates ,x y on the Cartesian coordinate plane of the vertices of a triangle

are 2,3 , 2,6 , and Z 7,3X Y . Calculate the perimeter of XYZ .

40 In the figure below, what is the value of the missing angles?

5

4

321

20

55

41 Calculate the perimeterRST if it is an equilateral triangle with = 4x - 8,RS

2 10,ST x and RT = 5x - 17 .

42 In the figure ,MQ NQ = 110MNP and 80NQP . Find all remaining angles.



D

CBA

4

2

5

Use the figure to answer.

43 Determine which postulate, if any, can be used to prove that ABD CBD when AD CD

and DB is an angle bisector. 44 Determine which postulate, if any, can be used to prove that ABD CBD when

BAD BCD and B is the midpoint of AC .

45 Determine which postulate, if any, can be used to prove that ABD CBD when AB CB

and DB AC . 46 Use the Pythagorean theorem to find the distance of the hypotenuse of the triangle below.

A. 4 3

B. 2 26

C. 2 13

D. 52



VT

S

YX

W

5

2

-2

C

B

A

47 The diagram below demonstrates the construction of copying an angle.

and TS TV are radii of circle T

and XW XY are radii of circle X

Which triangle congruence pattern can be used to justify that STV WXY ?

Use the figure to answer. 48 In the triangle graphed above, what is the slope of line segment AB? 49 In the triangle graphed above, what is the slope of line segment BC? 50 Using the answers from the previous two questions to classifyABC .



GF

K

H

xy

2 – 3n

2 + 2n

3

4

6

5

4

5

10

51 Find m KGH if GK bisects FGH , 7 3m FGK w and 104FGH .

52 Find the length of each side of the triangle below if the perimeter is 49 units. 53 Find the surface area and volume of the solid.

54 Find the volume of the solid.

55 What is the relationship between plane B and MN ?



10 yd

16 yd

20 yd

14 m

14 m19 m

19 m

32

24 24

M

N

P

(–3, 0)

O

(0, 4)

(3, 0)

(0, –3)

Q

x

y

56 The measures of two complementary angles are 6 3y and 4 13y . Find the measure of each

angle. 57 Find the area of the figure. 58 Find the area of the figure. 59 Find the area of the figure.

60 Find the slope of MN .



F

GH

F'

G'H'

x

y

14 in.

12.8 in.

24 m

30 m

20 m

17 m

24 m

37 m

61 Identify the congruence transformation as a flip, turn, or slide. 62 Find the volume of the figure. 63 Find the volume of the figure.

64 Find the volume of the figure. 65 Find the lateral area of the figure.



O NL

M ( , )

(0, 0) (2 , 0)

b

b

c

x

y

O NM

L ( , )

(0, 0) (2 , 0)

b

b

c

x

y

O

L

M

N (0, 2 )

(0, 0)

( )

b

c, b

x

y

O

N

M

L(0, 2 )

(0, 0)

( )

b

c, b

x

y

54

8

66 Find the area of the figure. 67 What are the missing coordinates of the triangle?

68 Position and label the triangle on the coordinate plane.

Isosceles LMN with base LN 2b units long a. b.

c. d.


APHS/MATH STOP ─ DO NOT GO ON

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