2019 (Aug.): NY Regents - Geometry - Sara Cowley | Library

Instructions

From the New York State Education Department. The University of the State of New York Regents High School Examination Geometry August 2019. Internet. Available from https://www.nysedregents.org/geometryre/819/geom82019-exam.pdf; accessed 3, May, 2023.

On the set of axes below, \overline{AB} is dilated by a scale factor of 5/2 centered at point P.
Which statement is always true?

The coordinates of the vertices of parallelogram CDEH are C(-5,5), D(2,5), E(-1,-1), and H(-8,-1). What are the coordinates of P, the point of intersection of diagonals \overline{CE} and \overline{DH}?

The coordinates of the endpoints of \overline{QS} are Q(-9,8) and S(9,-4). Point R is on \overline{QS} such that QR:RS is in the ratio of 1:2. What are the coordinates of point R?

If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is

In the diagram below of \triangle ACD, \overline{DB} is a median to \overline{AC}, and \overline{AB} \cong \overline{DB}.

If m\angle DAB = 32\degree, what is m\angle BDC?

What are the coordinates of the center and the length of the radius of the circle whose equation is x^{2}+y^{2}=8x-6y+39?

In the diagram below of parallelogram ABCD, \overline{AFGB}, \overline{CF} bisects \angle{DCB}, \overline{DG} bisects \angle{ADC}, and \overline{CF} and \overline{DG} intersect at E.
If m\angle{B}=75\degree, then the measure of \angle{EFA} is

What is an equation of a line that is perpendicular to the line whose equation is 2y+3x=1?

Triangles ABC and RST are graphed on the set of axes below.
Which sequence of rigid motions will prove \triangle{ABC}\cong\triangle{RST}?

If the line represented by y=-\frac{1}{4}x-2 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?

Square MATH has a side length of 7 inches. Which three-dimensional object will be formed by continuously rotating square MATH around side \overline{AT}?

Circle O with a radius of 9 is drawn below. The measure of central angle AOC is 120\degree.
What is the area of the shaded sector of circle O?

In quadrilateral QRST, diagonals \overline{QS} and \overline{RT} intersect at M. Which statement would always prove quadrilateral QRST is a parallelogram?

A standard-size golf ball was a diameter of 1.680 inches. The material used to make the golf ball weighs 0.6523 ounce per cubic inch. What is the weight, to the nearest hundredth of an ounce, of one golf ball?

Chelsea is sitting 8 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36\degree. If her line of sight starts 1.5 feet above ground, how tall is the tree, to the nearest foot?

In the diagram below of right triangle ABC, altitude \overline{CD} intersects hypotenuse \overline{AB} at D.

A countertop for a kitchen is modeled with the dimensions shown below. An 18-inch by 21-inch rectangle will be removed for the installation of the sink.
What is the area of the top of the installed countertop, to the nearest square foot?

In the diagram below, \overline{BC} connects points B and C on the congruent sides of isosceles triangle ADE, such that \triangle{ABC} is isosceles with vertex angle A.
If AB=10, BD=5, and DE=12, what is the length of \overline{BC}?

In \triangle{ABC} below, angle C is a right angle.
Which statement must be true?

In right triangle RST, altitude \overline{TV} is drawn to hypotenuse \overline{RS}.
If RV=12 and RT=18, what is the length of \overline{SV}?

What is the volume, in cubic centimeters, of a right square pyramid with base edges that are 64 cm long and a slant height of 40 cm?

In the diagram below, chords \overline{PQ} and \overline{RS} of circle O intersect at T.
Which relationship must always be true?

A rhombus is graphed on the set of axes below.
Which transformation would carry the rhombus onto itself?

A 15-foot ladder leans against a wall and makes an angle of 65\degree with the ground. What is the horizontal distance from the wall to the base of the ladder, to the nearest tenth of a foot?

Part II

Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

In parallelogram ABCD shown below, m\angle{DAC}=98\degree and m\angle{ACD}=36\degree.
What is the measure of angle B? Explain why.

An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles, as modeled below.
To the nearest tenth of a degree, what was the angle of elevation?

On the set of axes below, \triangle{ABC}\cong\triangle{DEF}.
Describe a sequence of rigid motions that maps \triangle{ABC} onto \triangle{DEF}.

The vertices of \triangle{ABC} have coordinates A(-2,-1), B(10,-1), and C(4,4). Determine and state the area of \triangle{ABC}. [The use of the set of axes in the box below is optional.]

Area = _______ 

Using the construction below, state the degree measure of \angle{CAD}. Explain why.

In the diagram below of circle K, secant \overline{PLKE} and tangent \overline{PZ} are drawn from external point P.
If m\overgroup{LZ}=56\degree, determine and state the degree measure of angle P.

A large water basin is in the shape of a right cylinder. The inside of the basin has a diameter of 8\frac{1}{4} feet and a height of 3 feet. Determine and state, to the nearest cubic foot, the number of cubic feet of water that it will take to fill the basin to a level of \frac{1}{2} foot from the top.

Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.

Triangle ABC is shown below. Using a compass and straightedge; construct the dilation of \triangle{ABC} centered at B with a scale factor of 2.
[Leave all construction marks]

Is the image of \triangle{ABC} similar to the original triangle? Explain why.

In the diagram below, \triangle{ABE}\cong\triangle{CBD}.

Prove \triangle{AFD}\cong\triangle{CFE}

A cargo trailer, pictured below, can be modeled by a rectangular prism and a triangular prism. Inside the trailer, the rectangular prism measures 6 feet wide and 10 feet long. The walls that form the triangular prism each measure 4 feet wide inside the trailer. The diagram below is of the floor, showing the inside measurements of the trailer.
If the inside height of the trailer is 6.5 feet, what is the total volume of the inside of the trailer, to the nearest cubic foot?

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Note that diagrams are not necessarily drawn to scale. For the question in this part, a correct numerical answer with no work shown will receive only 1 credit.

The coordinates of the vertices of \triangle{ABC} are A(1,2), B(-5,3), and C(-6,-3).

Part 1:
Prove that \triangle{ABC} is isosceles.
[The use of the set of axes on the Show Your Work space is optional.]

Part 2:
State the coordinates of point D such that quadrilateral ABCD is a square.

Part 3:
Prove that your quadrilateral ABCD is a square.
[The use of the set of axes on the Show Your Work space is optional.]

2019 (Aug.): NY Regents - Geometry

On the set of axes below, \overline{AB} is dilated by a scale factor of 5/2 centered at point P.Which statement is always true?

The coordinates of the vertices of parallelogram CDEH are C(-5,5), D(2,5), E(-1,-1), and H(-8,-1). What are the coordinates of P, the point of intersection of diagonals \overline{CE} and \overline{DH}?

The coordinates of the endpoints of \overline{QS} are Q(-9,8) and S(9,-4). Point R is on \overline{QS} such that QR:RS is in the ratio of 1:2. What are the coordinates of point R?

If the altitudes of a triangle meet at one of the triangle’s vertices, then the triangle is

In the diagram below of \triangle ACD, \overline{DB} is a median to \overline{AC}, and \overline{AB} \cong \overline{DB}.If m\angle DAB = 32\degree, what is m\angle BDC?

What are the coordinates of the center and the length of the radius of the circle whose equation is x^{2}+y^{2}=8x-6y+39?

In the diagram below of parallelogram ABCD, \overline{AFGB}, \overline{CF} bisects \angle{DCB}, \overline{DG} bisects \angle{ADC}, and \overline{CF} and \overline{DG} intersect at E.If m\angle{B}=75\degree, then the measure of \angle{EFA} is

What is an equation of a line that is perpendicular to the line whose equation is 2y+3x=1?

Triangles ABC and RST are graphed on the set of axes below.Which sequence of rigid motions will prove \triangle{ABC}\cong\triangle{RST}?

If the line represented by y=-\frac{1}{4}x-2 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?

Square MATH has a side length of 7 inches. Which three-dimensional object will be formed by continuously rotating square MATH around side \overline{AT}?

Circle O with a radius of 9 is drawn below. The measure of central angle AOC is 120\degree.What is the area of the shaded sector of circle O?

In quadrilateral QRST, diagonals \overline{QS} and \overline{RT} intersect at M. Which statement would always prove quadrilateral QRST is a parallelogram?

A standard-size golf ball was a diameter of 1.680 inches. The material used to make the golf ball weighs 0.6523 ounce per cubic inch. What is the weight, to the nearest hundredth of an ounce, of one golf ball?

Chelsea is sitting 8 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36\degree. If her line of sight starts 1.5 feet above ground, how tall is the tree, to the nearest foot?

In the diagram below of right triangle ABC, altitude \overline{CD} intersects hypotenuse \overline{AB} at D.

A countertop for a kitchen is modeled with the dimensions shown below. An 18-inch by 21-inch rectangle will be removed for the installation of the sink. What is the area of the top of the installed countertop, to the nearest square foot?

In the diagram below, \overline{BC} connects points B and C on the congruent sides of isosceles triangle ADE, such that \triangle{ABC} is isosceles with vertex angle A.If AB=10, BD=5, and DE=12, what is the length of \overline{BC}?

In \triangle{ABC} below, angle C is a right angle.Which statement must be true?

In right triangle RST, altitude \overline{TV} is drawn to hypotenuse \overline{RS}.If RV=12 and RT=18, what is the length of \overline{SV}?

What is the volume, in cubic centimeters, of a right square pyramid with base edges that are 64 cm long and a slant height of 40 cm?

In the diagram below, chords \overline{PQ} and \overline{RS} of circle O intersect at T.Which relationship must always be true?

A rhombus is graphed on the set of axes below.Which transformation would carry the rhombus onto itself?

A 15-foot ladder leans against a wall and makes an angle of 65\degree with the ground. What is the horizontal distance from the wall to the base of the ladder, to the nearest tenth of a foot?

Part II

In parallelogram ABCD shown below, m\angle{DAC}=98\degree and m\angle{ACD}=36\degree.What is the measure of angle B? Explain why.

An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles, as modeled below.To the nearest tenth of a degree, what was the angle of elevation?

On the set of axes below, \triangle{ABC}\cong\triangle{DEF}.Describe a sequence of rigid motions that maps \triangle{ABC} onto \triangle{DEF}.

Using the construction below, state the degree measure of \angle{CAD}. Explain why.

In the diagram below of circle K, secant \overline{PLKE} and tangent \overline{PZ} are drawn from external point P.If m\overgroup{LZ}=56\degree, determine and state the degree measure of angle P.

Triangle ABC is shown below. Using a compass and straightedge; construct the dilation of \triangle{ABC} centered at B with a scale factor of 2.[Leave all construction marks]Is the image of \triangle{ABC} similar to the original triangle? Explain why.

In the diagram below, \triangle{ABE}\cong\triangle{CBD}.Prove \triangle{AFD}\cong\triangle{CFE}

On the set of axes below, \overline{AB} is dilated by a scale factor of 5/2 centered at point P.
Which statement is always true?

In the diagram below of \triangle ACD, \overline{DB} is a median to \overline{AC}, and \overline{AB} \cong \overline{DB}.

If m\angle DAB = 32\degree, what is m\angle BDC?

In the diagram below of parallelogram ABCD, \overline{AFGB}, \overline{CF} bisects \angle{DCB}, \overline{DG} bisects \angle{ADC}, and \overline{CF} and \overline{DG} intersect at E.
If m\angle{B}=75\degree, then the measure of \angle{EFA} is

Triangles ABC and RST are graphed on the set of axes below.
Which sequence of rigid motions will prove \triangle{ABC}\cong\triangle{RST}?

Circle O with a radius of 9 is drawn below. The measure of central angle AOC is 120\degree.
What is the area of the shaded sector of circle O?

A countertop for a kitchen is modeled with the dimensions shown below. An 18-inch by 21-inch rectangle will be removed for the installation of the sink.
What is the area of the top of the installed countertop, to the nearest square foot?

In the diagram below, \overline{BC} connects points B and C on the congruent sides of isosceles triangle ADE, such that \triangle{ABC} is isosceles with vertex angle A.
If AB=10, BD=5, and DE=12, what is the length of \overline{BC}?

In \triangle{ABC} below, angle C is a right angle.
Which statement must be true?

In right triangle RST, altitude \overline{TV} is drawn to hypotenuse \overline{RS}.
If RV=12 and RT=18, what is the length of \overline{SV}?

In the diagram below, chords \overline{PQ} and \overline{RS} of circle O intersect at T.
Which relationship must always be true?

A rhombus is graphed on the set of axes below.
Which transformation would carry the rhombus onto itself?

In parallelogram ABCD shown below, m\angle{DAC}=98\degree and m\angle{ACD}=36\degree.
What is the measure of angle B? Explain why.

An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles, as modeled below.
To the nearest tenth of a degree, what was the angle of elevation?

On the set of axes below, \triangle{ABC}\cong\triangle{DEF}.
Describe a sequence of rigid motions that maps \triangle{ABC} onto \triangle{DEF}.

In the diagram below of circle K, secant \overline{PLKE} and tangent \overline{PZ} are drawn from external point P.
If m\overgroup{LZ}=56\degree, determine and state the degree measure of angle P.

Triangle ABC is shown below. Using a compass and straightedge; construct the dilation of \triangle{ABC} centered at B with a scale factor of 2.
[Leave all construction marks]

Is the image of \triangle{ABC} similar to the original triangle? Explain why.

In the diagram below, \triangle{ABE}\cong\triangle{CBD}.

Prove \triangle{AFD}\cong\triangle{CFE}