Parti 1 In the diagram below, AABC

Parti

Answer all 28 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [56]

1 In the diagram below, AABC = AXYZ.

Use this space for computations.

Which two statements identify corresponding congruent parts for these triangles?

(1) AB =XY and AC = £Y

(2) AB = YZ and ZC = AX

(3) BC=XY and AA = AY

BC = YZandAA = AX

A support beam between the floor and ceiling of a house forms a 90° angle with the floor. The builder wants to make sure that the floor and ceiling are parallel. Which angle should the support beam form with the ceiling

(1) 45°

(2) 60°

(3) 90°

(4) 180°

J

Geometry - August '10 m

3 In the diagram below, the vertices of ADEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of AABC is 36 cm.


3h 3 JV . jQ

19 Q

J^ ^

What is the length, in centimeters, of £F?

@ 6 (3) 18

(2) 12 (4) 4

4 What is the solution of the following system of equations?

y = {x + 3)2 - 4

y = 2x + 5

(1) (0,-4) (3) ( -4 , -3 ) and (0,5)

(2) (-4,0) (4) ( -3 , -4 ) and (5,0)

Geometry - August '10 [3] [OVER]

Use this space for 5 One step in a construction uses the endpoints of AB to create arcs computations.

with the same radii. The arcs intersect above and below the segment. What is the relationship of AB and the line connecting the points of intersection of these arcs?

(1) collinear

(2) congruent

(3) parallel

Q) perpendicular

6 If AABC ~ AZXY, mAA = 50, and mAC = 30, what is mAX?

(1) 30 (3) 80 b t \ j f D (2) 50 @ 100 / ^ ^ ^ _ r ^

100

Geometry - August '10 [4J

7 In the diagram below of AAGE and AOLD, AGAE = ALOD, and AE = OD.


To prove that AAGE and AOLD are congruent by SAS, what other information is needed?

(1) GE = LD

2\ AG = OL

(3) AAGE = AOLD

(4) AAEG = AODL

8 Point A is not contained in plane rB. How many lines can be drawn through point A that will be perpendicular to plane 15?

LU one (3) zero

(2) two (4) infinite

fi

V" (b

9 The equation of a circle is x2 + ((/ and radius of the circle?

7)2 = 16. What are the center

^ 7 center = (0,7); radius = 4

(2) center = (0,7); radius = 16

(3) center = (0,-7); radius = 4

(4) center = (0,-7); radius = 16


10 What is an equation of the line that passes through the point (7,3) and is parallel to the line 4x + 2y = 10?


(i) y = & -1

(2) y = -h + f

(3) y = 2x - 11

g) t/ = -2x + 17

u = oox-+b

11 In AABC, AB = 7, BC = 8, and AC = 9. Which list has the angles of AABC in order from smallest to largest? n

(1) AA, AB, AC (3) AC, AB, AA

(2) AB, AA, AC @ AC, AA, AB

A"

12 Tangents PA and PB are drawn to circle O from an external point, P, and radii OA and OB are drawn. If mZAPB = 40, what is the measure of ZAOB? A

© 140° (3) 70°

(2) 100° (4) 50° wo

13 What is the length of the line segment with endpoints A(—6,4) and B(2,-5)?

(1) Vl3 (3) V72

(2) Vl7 Q Vl45

d̂ i^w

Geometry - August '10 |6|

14 The lines represented by the equations y + jrX = 4 and 3x + 6ij = 12 are " .

(1) the same line

(D parallel

(3) perpendicular

(4) neither parallel nor perpendicular


15 A transformation of a polygon that always preserves both length and orientation is

(1) dilation (3) line reflection

/^) translation (4) glide reflection

16 In which polygon does the sum of the measures of the interior angles equal the sum of the measures of the exterior angles?

(1) triangle (3) octagon SUYT) ^ - 3 ^ (kim^)

(2) hexagon @ quadrilateral ^ ^ ^ ^ 0 m

([[iadr\\(*4ufoJ6


17 In the diagram below of circle O, chords AB and CD intersect at £. Use this space for

computations.

-Vx - (p[io)

If CE = 10, ED = 6, and AE = 4, what is the length of EB?

p 15 (3) 6.7

2) 12 (4) 2.4

18 In the diagram below of AABC, medians AD, BE, and CF intersect atG.

If CE = 24, what is the length of EG?

© 8 (3) 12

(2) 10 (4) 16

Geometry - August '10 [<SJ

Use this space for 19 If a line segment has endpoints A(3x + 51Sy) and B(x - 1, ~y), what computations.

are the coordinates of the midpoint of AB?

(1) (x + 3, 2y) (3) (2x + 3, y) P i ^ l ^ L - 1 J ^

© (2x + 2,y) (4) (4x + 4, 2y)

(^•^--(^^

20 If the surface area of a sphere is represented by 144-77, what is the volume in terms of TT? ^^ .,. /

(1) 3 6 . (3) 216 . ^ - ' ^

(2) 4 8 . © 288ir I^^TT = ^TTf9

3fc = r ^ (s-r

21 Which transformation of the line x = 3 results in an image that is perpendicular to the given line? A y - 3

;i) r.

y-axis

y =x

(4) rv

z.3

V


Use this space for 22 In the diagram below of regular pentagon ABCDE, EB is drawn. computations.

5

10) - / o f

19 5 c I^L 5

75

^3^

What is the measure of AAEB?

© 36° (3) 72°

(2) 54° (4) 108°

23 AABC is similar to ADEE. The ratio of the length of AB to the length of DE is 3:1. Which ratio is also equal to 3:1?

m mAA /o) area of AABC { ' mAD K ' area of ADEF

m Z g ^ perimeter of AABC K ' mZF ^ perimeter of ADFF

24 What is the slope of a line perpendicular to the line whose equation is 2y = -6x + 8?

(2) \ (4) - 6

y--^w

Geometry - August '10 [10]

25 In the diagram below of circle C, mQT = 140 and mZ.P = 40.


HO

x-lpO WhatismBS?

(1) 50

© 60 (3) 90

(4) 100

26 Which statement is logically equivalent to "If it is warm, then I go

swimming"? t O A ^ OU+, ̂ - ^ ^M+cJl ^

(1) If I go swimming, then it is warm.

(2) If it is warm, then I do not go swimming.

(P) If I do not go swimming, then it is not warm.

(4) If it is not warm, then I do not go swimming.

rugose


27 In the diagram below of AACP, BE || AT.


3_ 1

3x

X

49 N

If CB = 3, CA = 10, and CE = 6, what is the length of EP?

(1) 5 (3) 20

f ) 14 (4) 26

28 Which geometric principle is used in the construction shown below?

in) The intersection of the angle bisectors of a triangle is the center of the inscribed circle.

(2) The intersection of the angle bisectors of a triangle is the center of the circumscribed circle.

(3) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle.

(4) The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.


Part II

Answer all 6 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12]

29 The diagram below shows isosceles trapezoid ABCD with AB || DC and AD and mABCD = 3x + 5, find mABAD.

BC. U mABAD = 2x

(3x + 5)^

Sx

D

+ 3x + 6 =

Sx-tff^

5x -

K--

9* :

l?D Itl? -116

= 35 --no

1 tr)4&f\T)^'7o

(

/


30 A right circular cone has a base with a radius of 15 cm, a vertical height of 20 cm, and a slant height of 25 cm. Find, in terms of IT, the number of square centimeters in the lateral area of the cone.

Lft-?>l6i[


31 In the diagram below of AHQP, side HP is extended through P to T, mAQPT = 6x + 20, mAHQP = x + 40, and mAPHQ = 4x - 5. Find mAQPT.

(x + 40)

(Not drawn to scale)

\6* x

m^o^r ^//Q


32 On the line segment below, use a compass and straightedge to construct equilateral triangle ABC. [Leave all construction marks.]


33 In the diagram below, car A is parked 7 miles from car B. Sketch the points that are 4 miles from car A and sketch the points that are 4 miles from car B. Label with an X all points that satisfy both conditions.

/

/

1 1 1

\

Car A •

\ /

1

i

\

\

/ \

] )

/

J

Car B )

J \ K

Geometry-August'10 [17] [OVER]

34 Write an equation for circle O shown on the graph below.

y A

J

_/ 7 ( [ T * -4-t A i ^v

X

i^ r

L * " " - ' "^-v. i ^ <

\ \ \

0 . 1 ^ • I -y /

/ /

. s ^^"^%. - " ^ X

ttnfr-- (-1,3)

V (xrt^Wy-^^J


Part III

Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12]

35 In the diagram below of quadrilateral ABCD with diagonal BD, mAA = 93, mZADB = 43, mAC = 3x + 5, mABDC = Explain your reasoning.

i

D

x/3 ifu

f q 3 -I3(P

5(P w

= x + 19, and mADBC = 2x + 6. Determine if AB is parallel to DC.

A B [93° V V / \

y^2x + 6)0\

/ t x + 19)0 (3x + 5)0\ 0

(px^3o-/f0 (01 = 160

X--96 XH9 = //</

/ S i n a oJHrncJle /o-ft//<x abatis ar^ | 1 CAWU^ >, /Ifel bC j


36 The coordinates of the vertices of AABC are A(l,3), B(-2,2), and C(0,-2). On the grid below, graph and label AA"B"C", the result of the composite transformation D9

0 T3 _2. State the coordinates of A", B", and C".

1 1 j

^ "̂

1

[ ; ; i

|

i i

i | j

i

i |

/

l r

a, ,--' \

\

\

^

I 1 i i N

^

c

/

A 1

6 1 , ^

\

i \[ x \ ,

i 1 i

\

\

^ ^

j I \ j

\

ic"

^i /

/

/

/

_, L

, L J

f N /

^ J J

K

i


37 In the diagram below, ABST is a 3-4-5 right triangle. The altitude, h, to the hypotenuse has been drawn. Determine the length oih.

3_ b

5b

b

b

5_ 3

1. * S

= IS

R.

•

3 /

/u / b

h

n

^ \ 4

S . Q ^ V a >v

5-1.k = 3,3

i.r h "" 3.9

b3= 5.7fo

h = a . i l


Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [6]

38 Given: Quadrilateral ABCD has vertices A(-5,6), B(6,6), C(8,-3), andD( -3 , -3 ) .

Prove: Quadrilateral ABCD is a parallelogram but is neither a rhombus nor a rectangle.

[The use of the grid below is optional. ]

MonJ Shoto opposih SioUsafi -^ fat all Q]dK art s . ^ 0 ^

^fe=J^yMHo? cu^/MrMfc-^ dcv-^y^ dm-- {i-uY*(0?

dftb = u 5

/m

'p

^ £

ZC^RS ^

(3,

^

m (be

$&&-{>

? {Q^-n

BG

/

W'ti a

-flb

opf&sih

i

0 S: H^

^

,.,.,

^7¥ -9

^ f e

6Cy flfe/fc

^ ^ ^ ^ f e ^

& mi d fhdYnhus

-q\3 -3)


Parti 1 In the diagram below, AABC

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