august-2016-geometry-1-to-5-nys-regents-common-core-solutions-worked-out-steps

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In the diagram below, lines ℓ, m, n, and p intersect line r.

Which statement is true?

(1) ℓ || n (3) m || p

(2) ℓ || p (4) m || n

2 Which transformation would not always produce an image that

would be congruent to the original figure?

(1) translation (3) rotation

(2) dilation (4) reflection

3 If an equilateral triangle is continuously rotated around one of its

medians, which 3-dimensional object is generated?

(1) cone (3) prism

(2) pyramid (4) sphere

4 In the diagram below, m∠BDC 100°, m∠A 50°, and computations.

m∠DBC 30°.

Which statement is true?

(1) ABD is obtuse. (3) m∠ABD 80°

(2) ABC is isosceles. (4) ABD is scalene.

5 Which point shown in the graph below is the image of point P after

a counterclockwise rotation of 90° about the origin?

(1) A (3) C

(2) B (4) D

y

x

D

C

P

B

A

B

A C D

Geometry (Common Core) – Aug. ’16 [3] [OVER]

Geometry (Common Core) – Aug. ’16 [4]

6 In ABC, where ∠C is a right angle, . What is sin B?

(1) (3)

(2) (4)

7 Quadrilateral ABCD with diagonals

___

AC and

___

BD is shown in the

diagram below.

Which information is not enough to prove ABCD is a parallelogram?

(1) AB

___

CD

___

and AB

___ || DC

___

(2) AB

___ CD

___ and BC

___

___

DA

(3) AB

___ CD

___ and BC

___ || AD

___

(4) AB

___ || DC

___

and BC

___ || AD

___

8 An equilateral triangle has sides of length 20. To the nearest tenth,

what is the height of the equilateral triangle?

(1) 10.0 (3) 17.3

(2) 11.5 (4) 23.1

5

21 A

B C

D

cos A = 21

5

21

2

2

5 21

5

Use this space for

computations.

9 Given: AEC, DEF, and

___

FE ⊥

___

CE

What is a correct sequence of similarity transformations that shows

AEC ~ DEF?

(1) a rotation of 180 degrees about point E followed by a horizontal

translation

(2) a counterclockwise rotation of 90 degrees about point E

followed by a horizontal translation

(3) a rotation of 180 degrees about point E followed by a dilation

with a scale factor of 2 centered at point E

(4) a counterclockwise rotation of 90 degrees about point E

followed by a dilation with a scale factor of 2 centered at point E

10 In the diagram of right triangle ABC, CD

___ intersects hypotenuse

AB

___

at D.

If AD 4 and DB 6, which length of

___

AC makes CD

___

⊥ AB

___

?

(1) (3)

(2) 2 10 (4) 4 2 2 6 2 15

D6 B

C

A 4

F

6

8 E

D

A

4

3

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