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1 What is the solution of the system of equations graphed below?What are the coordinates of the midpoint of the line segment with

endpoints (2,5) and (8,3)?

(1) (3,4) (3) (5,4)

(2) (3,1) (4) (5,1)

As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon ABCDEF Under this transformation, which property is not preserved?

(1) area (3) orientation

(2) distance (4) angle measure

4 In 4 In the diagram of ABC below,

___

BD is drawn to side

___

AC. If m∠A 35, m∠ABD 25, and m∠C 60, which type of triangle

is BCD?

(1) equilateral (3) obtuse

(2) scalene (4) right In the diagram below of rhombus ABCD, the diagonals If AC 18 and BD 24, what is the length of one side of rhombus

ABCD?

(1) 15 (3) 24

(2) 18 (4) 30

6 What are the truth values of the statement “Opposite angles of a

trapezoid are always congruent” and its negation?

(1) The statement is true and its negation is true.

(2) The statement is true and its negation is false.

(3) The statement is false and its negation is true.

(4) The statement is false and its negation is false.What is the length of a line segment whose endpoints have

coordinates (5,3) and (1,6)?In the diagram below of isosceles ABC, the measure of vertex angle B is 80°. If

___

AC extends to point D, what is m∠BCD? A student used a compass and a straightedge to construct CE

___

in

ABC as shown below. Which statement must always be true for this construction?

(1) ∠CEA ∠CEB (3) AE

___

BE

___

(2) ∠ACE ∠BCE (4) EC

___

AC

___

10 In ABC, AB 4, BC 7, and AC 10. Which statement is true?

(1) m∠B m∠C m∠A (3) m∠C m∠B m∠A

(2) m∠B m∠A m∠C (4) m∠C m∠A m∠B A circle whose center has coordinates (3,4) passes through the

origin. What is the equation of the circle?

(1) (x +3)2 (y 4)2 5

(2) (x +3)2 (y 4)2 25

(3) (x -3)2 (y 4)2 5

(4) (x -3)2 (y 4)2 25 Point W is located in plane R . How many distinct lines passing

through point W are perpendicular to plane R ?

(1) one (3) zero

(2) two (4) infinite In the diagram below, line is parallel to line m, and line w is a

transversal. If m∠2 3x 17 and m∠3 5x 21, what is m∠1?

(1) 19 (3) 74

(2) 23 (4) 86 The diagram below is a graph of circle O.In isosceles trapezoid QRST shown below, QR

___

and TS

___

are bases.

If m∠Q 5x 3 and m∠R 7x 15, what is m∠Q?

(1) 83 (3) 16

(2) 48 (4) 9

T S

Q Are What are the coordinates of the point of intersection of the medians

of ABC?

(1)Given the statement, “If a number has exactly two factors, it is a

prime number,” what is the contrapositive of this statement?

(1) If a number does not have exactly two factors, then it is not a

prime number.

(2) If a number is not a prime number, then it does not have exactly

two factors.

(3) If a number is a prime number, then it has exactly two factors.

(4) A number is a prime number if it has exactly two factors.Which graph represents a circle whose equation is

(x 2)2 (y 4)2 4?If two sides of a triangle have lengths of 4 and 10, the third side

could be

(1) 8 (3) 16

(2) 2 (4) 4The lines represented by the equations 4x 6y 6 and computations.

y 2 __

3 x 1 are

(1) parallel

(2) the same line

(3) perpendicular

(4) intersecting, but not perpendicularIn the diagram below of ABC, DE

___

|| AB Parallelogram ABCD with diagonals AC

___

and BD

___

intersecting at E is

shown below. Which statement must be true?

(1) BE

___

CE

___

(3) AB

___

BC

___

(2) ∠BAE ∠DCE (4) ∠DAE ∠CBE

23 In the diagram below of circle O, m∠ABC 24.

What is m∠AOC?

(1) 12 (3) 48

(2) 24 (4) 60

24 Triangle ABC is the image of ABC after a dilation of 2.

Which statement is true?

(1) AB AB (3) m∠B m∠B

(2) BC 2(BC) (4) m∠A 1 __

2 (m∠A)

A

B

C Triangle ABC is the image of ABC after a dilation of 2.

Which statement is true?

(1) AB AB (3) m∠B m∠B

(2) BC 2(BC) (4) m∠A 1 __

2 (m∠A) In the diagram of the circle below, AD computations.

___

|| BC

___

, (5x 30)°, and

(9x 10)°. The bases of a prism are right trapezoids, as shown in the diagram

below.

Which In the diagram below, computations.

__

AB

__

is the image of AB

___

under which

single transformation? (1) dilation (3) translation

(2) rotation (4) glide reflection

28 For which diagram is the statement ABC ~ADE not always true?

Tagged under: Geometry Regents,New York State,2015,examination,graphing equations,points,quadratic,line,coordinates,midpoint,segment,endpoints,diagram,hexagon,reflected,transformation,preserved,orientation,angle measure,area,distance,equilateral,triangle,obtuse,scalene,rhombus,intersect,logic,converse,contrapositive,inverse,conditional,true,false,truth values,length,vertex,isoceles,bisector,construct,triangle inequality,circle,perpendicular,plane,paralle,alternate

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