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2023: NY Regents - Geometry

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Last updated 3 months ago
35 questions
2
G.CO.5
2
G.GMD.4
2
G.CO.10
2
G.SRT.7
2
G.CO.10
2
G.MG.2
2
G.SRT.6
2
G.SRT.5
2
G.CO.11
2
G.GMD.3
2
G.CO.3
2
G.C.2
2
G.GPE.5
2
G.GPE.1
2
G.SRT.5
2
G.CO.10
2
G.C.5
2
G.CO.11
2
G.SRT.1.a
2
G.GMD.3
2
G.CO.10
2
G.SRT.1.a
2
G.C.2
2
G.SRT.3
2
G.CO.12
2
G.CO.5
2
G.SRT.8
2
G.GPE.6
2
G.SRT.5
2
G.GMD.3
2
G.GPE.7
4
G.GMD.3
4
G.SRT.5
4
G.SRT.8
6
G.GPE.4
From the New York State Education Department. The University of the State of New York Regents High School Examination Geometry January 2023. Internet. Available from https://www.nysedregents.org/geometryre/123/geom12023-exam.pdf; accessed 3, May, 2023.
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18.

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19.

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21.

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22.

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23.

Question 24
24.

Question 25
25.

Using a compass and straightedge, construct the angle bisector of \angle{ABC}.
[Leave all construction marks.]

Utilize the embedded tool above and take a screenshot/picture of your finished work. Upload that image as your answer in the Show Your Work space.

Question 26
26.

On the set of axes below, \triangle{ABC} and \triangle{DEF} are graphed.

Describe a sequence of rigid motions that would map \triangle{ABC} onto \triangle{DEF}.

Question 27
27.
As shown in the diagram below, a symmetrical roof frame rises 4 feet above a house and has a width of 24 feet.

Determine and state, to the nearest degree, the angle of elevation of the roof frame.

Angle of elevation is _______ degrees.
Question 28
28.

Directed line segment AB has endpoints whose coordinates are A(-2,5) and B(8,-1).
Determine and state the coordinates of P, the point which divides the segment in the ratio 3:2.
[The use of the set of axes in the Show Your Work space is optional.]

Question 29
29.

In \triangle{ABC}, AB=5, AC=12, and m\angle{A}=90\degree. In \triangle{DEF}, m\angle{D}=90\degree, DF=12, and EF=13. Brett claims \triangle{ABC}\cong\triangle{DEF} and \triangle{ABC}\sim\triangle{DEF}.

Is Brett correct? Explain why.

Question 30
30.
The volume of a triangular prism is 70 in3. The base of the prism is a right triangle with one leg whose measure is 5 inches. If the height of the prism is 4 inches, determine and state the length, in inches, of the other leg of the triangle.

_______ inches
Question 31
31.

Triangle ABC with coordinates A(-2,5), B(4,2), and C(-8,-1) is graphed on the set of axes below.

Determine and state the area of \triangle{ABC}.

Question 32
32.
Sally and Mary both get ice cream from an ice cream truck. Sally's ice cream is served as a cylinder with a diameter of 4 cm and a total height of 8 cm. Mary's ice cream is served as a cone with a diameter of 7 cm and a total height of 12.5 cm. Assume that ice cream fills Sally's cylinder and Mary's cone.


Who was served more ice cream, Sally or Mary? _______
Justify your answer: _______
Determine and state how much more is served in the larger ice cream than the smaller ice cream, to the nearest cubic centimeter: _______
Question 33
33.

Given: \triangle{AEB} and \triangle{DFC}, \overline{ABCD}, \overline{AE}\parallel\overline{DF}, \overline{EB}\parallel\overline{FC}, \overline{AC}\cong\overline{DB}

Prove: \triangle{EAB}\cong\triangle{FDC}

Question 34
34.
Barry wants to find the height of a tree that is modeled in the diagram below, where \angle{C} is a right angle. The angle of elevation from point A on the ground to the top of the tree, H, is 40\degree. The angle of elevation from point B on the ground to the top of the tree, H, is 80\degree. The distance between points A and B is 85 feet.

Barry claims that \triangle{ABH} is isosceles. Explain why Barry is correct: _______

Determine and state, to the nearest foot, the height of the tree: _______
Question 35
35.

Given: Triangle DUC with coordinates D(-3,-1), U(-1,8), and C(8,6)

Part 1:
Prove: \triangle{DUC} is a right triangle
[The use of the set of axes in the Show Your Work space is optional.]

Part 2:
Point U is reflected over \overline{DC} to locate its image point, U', forming quadrilateral DUCU'.
Prove quadrilateral DUCU' is a square.

In the diagram below, a line reflection followed by a rotation maps \triangle{ABC} onto \triangle{DEF}.
Which statement is always true?
\overline{BC}\cong\overline{EF}
\overline{AC}\cong\overline{DE}
\angle{A}\cong\angle{F}
\angle{B}\cong\angle{D}
A circle is continuously rotated about its diameter. Which three-dimensional object will be formed?
cone
prism
sphere
cylinder
In the diagram below of \triangle{CER}, \overline{LA}\parallel\overline{CR}.
If CL=3.5, LE=7.5, and EA=9.5, what is the length of \overline{AR}, to the nearest tenth?
5.5
4.4
3.0
2.8
Right triangle ABC is shown below.

Which trigonometric equation is always true for triangle ABC?
In the diagram of \triangle{ABC} below, \overline{AE} bisects angle BAC, and altitude \overline{BD} is drawn.
If m\angle{C}=50\degree and m\angle{ABC}=60\degree, m\angle{FEB} is
35\degree
40\degree
55\degree
85\degree
A jewelry company makes copper heart pendants. Each heart uses 0.75 in3 of copper and there is 0.323 pound of copper per cubic inch. If copper costs $3.68 per pound, what is the total cost for 24 copper hearts?
$5.81
$21.40
$66.24
$205.08
In right triangle LMN shown below, m\angle{M}=90\degree, MN=12, and LM=16.
The ratio of \mathrm{cos} N is
12/20
16/20
12/16
16/12
In \triangle{ABC} below, \overline{DE} is drawn such that D and E are on \overline{AB} and \overline{AC}, respectively.
If \overline{DE}\parallel\overline{BC}, which equation will always be true?
\frac{AD}{DE}=\frac{DB}{BC}
\frac{AD}{DE}=\frac{AB}{BC}
\frac{AD}{BC}=\frac{DE}{DB}
\frac{AD}{BC}=\frac{DE}{AB}
Which polygon does not always have congruent diagonals?
square
rectangle
rhombus
isosceles trapezoid
If the circumference of a standard lacrosse ball is 19.9 cm, what is the volume of this ball, to the nearest cubic centimeter?
42
133
415
1065
Which polygon always has a minimum rotation of 180° about its center to carry it onto itself?
Circle O is drawn below with secant \overline{BCD}. The length of tangent \overline{AD} is 24.

If the ratio of DC:CB is 4:5, what is the length of \overline{CB}?
36
20
16
4
The equation of a line is 3x-5y=8. All lines perpendicular to this line must have a slope of
3/5
5/3
-\frac{3}{5}
-\frac{5}{3}
What are the coordinates of the center and length of the radius of the circle whose equation is x^{2}+y^{2}+2x-16y+49=0?
center (1,-8) and radius 4
center (-1,8) and radius 4
center (1,-8) and radius 16
center (-1,8) and radius 16
In the diagram below of right triangle MDL, altitude \overline{DG} is drawn to hypotenuse \overline{ML}.

If MG=3 and GL=24, what is the length of \overline{DG}?
8
9
\sqrt{63}
\sqrt{72}
Segment AB is the perpendicular bisector of \overline{CD} at point M.
Which statement is always true?
\overline{CB}\cong\overline{DB}
\overline{CD}\cong\overline{AB}
\triangle{ACD}\sim\triangle{BCD}
\triangle{ACM}\sim\triangle{BCM}
In the diagram below of circle O, \overline{AC} and \overline{BC} are chords, and m\angle{ACB}=70\degree.

If OA=9, the area of the shaded sector AOB is
3.5\pi
7\pi
15.75\pi
31.5\pi
Quadrilateral BEST has diagonals that intersect at point D. Which statement would not be sufficient to prove quadrilateral BEST is a parallelogram?
\overline{BD}\cong\overline{SD} and \overline{ED}\cong\overline{TD}
\overline{BE}\cong\overline{ST} and \overline{ES}\cong\overline{TB}
\overline{ES}\cong\overline{TB} and \overline{BE}\parallel\overline{TS}
\overline{ES}\parallel\overline{BT} and \overline{BE}\parallel\overline{TS}
The equation of line t is 3x-y=6. Line m is the image of line t after a dilation with a scale factor of 1/2 centered at the origin.
What is an equation of line m?
y=\frac{3}{2}x-3
y=\frac{3}{2}x-6
y=3x+3
y=3x-3
A cylindrical pool has a diameter of 16 feet and height of 4 feet.
The pool is filled to 1/2 foot below the top. How much water does the pool contain, to the nearest gallon? [1 ft3 = 7.48 gallons]
704
804
5264
6016
The area of \triangle{TAP} is 36 cm2. A second triangle, JOE, is formed by connecting the midpoints of each side of \triangle{TAP}. What is the area of \triangle{JOE}, in square centimeters?
9
12
18
27
On the set of axes below, the endpoints of \overline{AB} have coordinates A(-3,4) and B(5,2).

If \overline{AB} is dilated by a scale factor of 2 centered at (3,5), what are the coordinates of the endpoints of its image, \overline{A'B'}?
A' (-7,5) and B' (9,1)
A' (-1,6) and B' (7,4)
A' (-6,8) and B' (10,4)
A' (-9,3) and B' (7,-1)
In the circle below, \overline {AD}, \overline{AC}, \overline{BC}, and \overline{DC} are chords, \overleftrightarrow{EDF} is tangent at point D, and \overline{AD}\parallel\overline{BC}.

Which statement is always true?
\angle{ADE}\cong\angle{CAD}
\angle{CDF}\cong\angle{ACB}
\angle{BCA}\cong\angle{DCA}
\angle{ADC}\cong\angle{ADE}
In the diagram below of \triangle{ABC}, D and E are the midpoints of \overline{AB} and \overline{AC}, respectively, and \overline{DE} is drawn.

Which methods could be used to prove \triangle{ABC}\sim\triangle{ADE}?
I and II, only
II and III, only
I and III, only
I, II, and III