The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY

Wednesday, January 29, 2014 — 9:15 a.m. to 12:15 p.m., only

Student our name and the name of your school on the lines above.

A separate answer sheet for Part I has been provided to you. Follow the

instructions from the proctor for completing the student information on your answer

sheet.

This examination has four parts, with a total of 38 questions. You must answer

all questions in this examination. Record your answers to the Part I multiple-choice

questions on the separate answer sheet. Write your answers to the questions in

Parts II, III, and IV directly in this booklet. All work should be written in pen,

except for graphs and drawings, which should be done in pencil. Clearly indicate

the necessary steps, including appropriate formula substitutions, diagrams, graphs,

charts, etc.

The formulas that you may need to answer some questions in this examination

are found at the end of the examination. This sheet is perforated so you may

remove it from this booklet.

Scrap paper is not permitted for any part of this examination, but you may use

the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph

paper is provided at the end of this booklet for any question for which graphing

may be helpful but is not required. You may remove this sheet from this booklet.

Any work done on this sheet of scrap graph paper will not be scored.

When you have completed the examination, you must sign the statement printed

at the end of the answer sheet, indicating that you had no unlawful knowledge of

the questions or answers prior to the examination and that you have neither given

nor received assistance in answering any of the questions during the examination.

Your answer sheet cannot be accepted if you fail to sign this declaration.

GEOMETRY

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

Notice...

A graphing calculator, a straightedge (ruler), and a compass must be available for you to use while

taking this examination.

GEOMETRY

The possession or use of any communications device is strictly prohibited when taking this

examination. If you have or use any communications device, no matter how briefly, your examination

will be invalidated and no score will be calculated for you.

1 The midpoint of AB

___

is M(4,2). If the coordinates of A are (6,4),

what are the coordinates of B?

(1) (1,3) (3) (5,1)

(2) (2,8) (4) (14,0)

2 Which diagram shows the construction of a 45° angle?

(1)

(2)

(3)

(4)

Use this space for

computations.

Part I

Answer all 28 questions in this part. Each correct answer will receive 2 credits. For each

statement or question, choose the word or expression that, of those given, best completes the

statement or answers the question. Record your answers on your separate answer sheet. [56]

Geometry -- January '14 [2]

Use this space for

3 What are the coordinates of the center and the length of the radius computations.

of the circle whose equation is (x 1)2 (y 5)2 16?

(1) (1,5) and 16 (3) (1,5) and 4

(2) (1,5) and 16 (4) (1,5) and 4

4 If distinct planes R and S are both perpendicular to line ℓ, which

statement must always be true?

(1) Plane R is parallel to plane S.

(2) Plane R is perpendicular to plane S.

(3) Planes R and S and line ℓ are all parallel.

(4) The intersection of planes R and S is perpendicular to line ℓ.

5 If ABC and its image, ABC, are graphed on a set of axes,

ABC ABC under each transformation except

(1) D2 (3) ry x

(2) R90° (4) T(2,3)

6 A right rectangular prism is shown in the diagram below.

Which pair of edges are not coplanar?

(1) BF

___

and CG

___

(3) EF

___

and CD

___

(2) BF

___

and DH

___

(4) EF

___

and BC

___

A

Geometry -- January '14 [3] [OVER]

Use this space for

7 How many points in the coordinate plane are 3 units from the computations.

origin and also equidistant from both the x-axis and the y-axis?

8 As shown below, the medians of ABC intersect at D.

If the length of BE

___

is 12, what is the length of BD

9 The solution of the system of equations y x2 2 and y x is

(1) (1,1) and (2,2) (3) (1,1) and (2,2)

(2) (2,2) and (1,1) (4) (2,2) and (1,1)

10 Line ℓ passes through the point (5,3) and is parallel to line k whose

equation is 5x y 6. An equation of line ℓ is

(1) y

1 __

5 x 2 (3) y

1 __

5 x 2

(2) y 5x 28 (4) y 5x 28

Geometry -- January '14 [4]

Use this space for

11 In the diagram below of quadrilateral ABCD, E and F are points computations.

on AB

___

and CD

___

, respectively, BE

___

DF

___

, and AE

___

CF

___

.

Which conclusion can be proven?

(1) ED

___

FB

___

(3) ∠A ∠C

(2) AB

___

CD

___

(4) ∠AED ∠CFB

12 In the diagram below, four pairs of triangles are shown.

Congruent corresponding parts are labeled in each pair.

Using only the information given in the diagrams, which pair of

triangles can not be proven congruent?

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