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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1.
In the diagram below, a line reflection followed by a rotation maps \triangle{ABC} onto \triangle{DEF}.
Which statement is always true?
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2.
A circle is continuously rotated about its diameter. Which three-dimensional object will be formed?
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3.
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?
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4.
Right triangle ABC is shown below.
Which trigonometric equation is always true for triangle ABC?
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5.
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
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6.
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?
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7.
In right triangle LMN shown below, m\angle{M}=90\degree, MN=12, and LM=16.
The ratio of \mathrm{cos} N is
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8.
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?
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9.
Which polygon does not always have congruent diagonals?
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10.
If the circumference of a standard lacrosse ball is 19.9 cm, what is the volume of this ball, to the nearest cubic centimeter?
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11.
Which polygon always has a minimum rotation of 180° about its center to carry it onto itself?
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12.
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}?
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13.
The equation of a line is 3x-5y=8. All lines perpendicular to this line must have a slope of
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14.
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?
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15.
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}?
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16.
Segment AB is the perpendicular bisector of \overline{CD} at point M.
Which statement is always true?
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17.
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
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18.
Quadrilateral BEST has diagonals that intersect at point D. Which statement would not be sufficient to prove quadrilateral BEST is a parallelogram?
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19.
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?
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20.
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]
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21.
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?
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22.
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'}?
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23.
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?
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24.
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}?
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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.
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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}.
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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.
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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.]
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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.
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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
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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}.
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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: _______
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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}
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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: _______
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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'.
