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More Lessons for the Regents High School Exam

More Lessons for Algebra

High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Common Core) Regents High School Examination August 2017.

### Geometry Common Core Regents New York State Exam - August 2017

The following are questions from the past paper
Regents High School Geometry, August 2017 Exam (pdf). Scroll down the page for the step by step solutions.

Geometry - August 2017 Regents - Questions and solutions 1 - 12

1. A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three dimensional object?

2. The image of DEF is D'E'F'. Under which transformation will the triangles not be congruent?

3. The vertices of square RSTV have coordinates R(-1,5), S(-3,1), T(-7,3), and V(-5,7). What is the perimeter of RSTV?

4. In the diagram below of circle O, chord is parallel to diameter AOB and mCD = 130.

5. In the diagram below, intersects at C, and AB || DE.

If CD = 6.6 cm, DE = 3.4 cm, CE = 4.2 cm, and BC = 5.25 cm, what is the length of AC, to the nearest hundredth of a centimeter?

6. As shown in the graph below, the quadrilateral is a rectangle.

Which transformation would not map the rectangle onto itself?

7. In the diagram below, triangle ACD has points B and E on sides AC and AD, respectively, such that BE || CD, AB = 1, BC = 3.5, and AD = 18. What is the length of AE, to the nearest tenth?

8. In the diagram below of parallelogram ROCK, m∠C is 70° and m∠ROS is 65°. What is m∠KSO?

9. In the diagram below, ∠GRS ≅ ∠ART, GR = 36, SR = 45, AR = 15, and RT = 18. Which triangle similarity statement is correct?

10. The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

11. Given ABC with m∠B = 62° and side AC extended to D, as shown below. Which value of x makes AB ≅ CB?

12. In the diagram shown below, PA is tangent to circle T at A, and secant PBC is drawn where point B is on circle T. If PB = 3 and BC = 15, what is the length of PA?

Geometry - August 2017 Regents - Questions and solutions 13 - 24

13. A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously rotated around a straight line to form an object whose volume is 150π. Which line could the rectangle be rotated around?

14. If ABCD is a parallelogram, which statement would prove that ABCD is a rhombus?

15. To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram below.

What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree?

16. In the diagram below of ABC, D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the ratio of the area of CFE to the area of CAB?

17. The coordinates of the endpoints of are A(-8,-2) and B(16,6). Point P is on AB. What are the coordinates of point P, such that AP:PB is 3:5?

18. Kirstie is testing values that would make triangle KLM a right triangle when LN is an altitude, and KM = 16, as shown below.

Which lengths would make triangle KLM a right triangle?

19. In right triangle ABC, m∠A = 32°, m∠B = 90°, and AC = 6.2 cm.

What is the length of BC, to the nearest tenth of a centimeter?

20. The 2010 U.S. Census populations and population densities are shown in the table below.

Based on the table above, which list has the states’ areas, in square miles, in order from largest to smallest?

21. In a right triangle, sin (40 - x)° cos (3x)°. What is the value of x?

22. A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be

23. In a circle with a diameter of 32, the area of a sector is 512π/3. The measure of the angle of the sector, in radians, is

24. What is an equation of the perpendicular bisector of the line segment shown in the diagram below?

Geometry - August 2017 Regents - Questions and solutions Parts 2-4

25. Sue believes that the two cylinders shown in the diagram below have equal volumes.

Is Sue correct? Explain why

26. In the diagram of rhombus PQRS below, the diagonals PR and QS intersect at point T, PR = 16, and QS = 30. Determine and state the perimeter of PQRS.

27. Quadrilateral MATH and its image M'A'T'H' are graphed on the set of axes below

Describe a sequence of transformations that maps quadrilateral MATH onto quadrilateral M'A'T'H'.

28. Using a compass and straightedge, construct a regular hexagon inscribed in circle O. [Leave all construction marks.]

29. The coordinates of the endpoints of are A(2,3) and B(5,–1). Determine the length of A'B', the image of AB, after a dilation of centered at the origin.

30. In the diagram below of ABC and XYZ, a sequence of rigid motions maps ∠A onto ∠X, ∠C onto ∠Z, and AC onto XZ.

Determine and state whether BC ≅ YZ. Explain why.

31. Determine and state the coordinates of the center and the length of the radius of a circle whose equation is x^{2} + y^{2} - 6x = 56 - 8y.

32. Triangle PQR has vertices P(-3,-1), Q(-1,7), and R(3,3), and points A and B are midpoints of PQ and RQ, respectively. Use coordinate geometry to prove that AB is parallel to PR and is half the length of PR.

[The use of the set of axes below is optional.]

33. In the diagram below of circle O, tangent EC is drawn to diameter AC. Chord BC is parallel to secant ADE, and chord AB is drawn.

Prove BC/CA = AB/EC

34. Keira has a square poster that she is framing and placing on her wall. The poster has a diagonal 58 cm long and fits exactly inside the frame. The width of the frame around the picture is 4 cm.

Determine and state the total area of the poster and frame to the nearest tenth of a square centimeter.

35. Isosceles trapezoid ABCD has bases DC and AB with nonparallel legs AD and BC. Segments AE, BE, CE, and DE are drawn in trapezoid ABCD such that ∠CDE ≅ ∠DCE, AE &prep; DE and BE &prep; CE.

Prove ADE ≅ BCE and prove AEB is an isosceles triangle.

36. A rectangular in-ground pool is modeled by the prism below. The inside of the pool is 16 feet wide and 35 feet long. The pool has a shallow end and a deep end, with a sloped floor connecting the two ends. Without water, the shallow end is 9 feet long and 4.5 feet deep, and the deep end of the pool is 12.5 feet long.

If the sloped floor has an angle of depression of 16.5 degrees, what is the depth of the pool at the deep end, to the nearest tenth of a foot?

Find the volume of the inside of the pool to the nearest cubic foot.

A garden hose is used to fill the pool. Water comes out of the hose at a rate of 10.5 gallons per minute. How much time, to the nearest hour, will it take to fill the pool 6 inches from the top? [1 ft^{3} = 7.48 gallons]

More Lessons for the Regents High School Exam

More Lessons for Algebra

High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Common Core) Regents High School Examination August 2017.

Geometry - August 2017 Regents - Questions and solutions 1 - 12

1. A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three dimensional object?

2. The image of DEF is D'E'F'. Under which transformation will the triangles not be congruent?

3. The vertices of square RSTV have coordinates R(-1,5), S(-3,1), T(-7,3), and V(-5,7). What is the perimeter of RSTV?

4. In the diagram below of circle O, chord is parallel to diameter AOB and mCD = 130.

5. In the diagram below, intersects at C, and AB || DE.

If CD = 6.6 cm, DE = 3.4 cm, CE = 4.2 cm, and BC = 5.25 cm, what is the length of AC, to the nearest hundredth of a centimeter?

6. As shown in the graph below, the quadrilateral is a rectangle.

Which transformation would not map the rectangle onto itself?

7. In the diagram below, triangle ACD has points B and E on sides AC and AD, respectively, such that BE || CD, AB = 1, BC = 3.5, and AD = 18. What is the length of AE, to the nearest tenth?

8. In the diagram below of parallelogram ROCK, m∠C is 70° and m∠ROS is 65°. What is m∠KSO?

9. In the diagram below, ∠GRS ≅ ∠ART, GR = 36, SR = 45, AR = 15, and RT = 18. Which triangle similarity statement is correct?

10. The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

11. Given ABC with m∠B = 62° and side AC extended to D, as shown below. Which value of x makes AB ≅ CB?

12. In the diagram shown below, PA is tangent to circle T at A, and secant PBC is drawn where point B is on circle T. If PB = 3 and BC = 15, what is the length of PA?

13. A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously rotated around a straight line to form an object whose volume is 150π. Which line could the rectangle be rotated around?

14. If ABCD is a parallelogram, which statement would prove that ABCD is a rhombus?

15. To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram below.

What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree?

16. In the diagram below of ABC, D, E, and F are the midpoints of AB, BC, and CA, respectively. What is the ratio of the area of CFE to the area of CAB?

17. The coordinates of the endpoints of are A(-8,-2) and B(16,6). Point P is on AB. What are the coordinates of point P, such that AP:PB is 3:5?

18. Kirstie is testing values that would make triangle KLM a right triangle when LN is an altitude, and KM = 16, as shown below.

Which lengths would make triangle KLM a right triangle?

19. In right triangle ABC, m∠A = 32°, m∠B = 90°, and AC = 6.2 cm.

What is the length of BC, to the nearest tenth of a centimeter?

20. The 2010 U.S. Census populations and population densities are shown in the table below.

Based on the table above, which list has the states’ areas, in square miles, in order from largest to smallest?

21. In a right triangle, sin (40 - x)° cos (3x)°. What is the value of x?

22. A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be

23. In a circle with a diameter of 32, the area of a sector is 512π/3. The measure of the angle of the sector, in radians, is

24. What is an equation of the perpendicular bisector of the line segment shown in the diagram below?

Geometry - August 2017 Regents - Questions and solutions Parts 2-4

25. Sue believes that the two cylinders shown in the diagram below have equal volumes.

Is Sue correct? Explain why

26. In the diagram of rhombus PQRS below, the diagonals PR and QS intersect at point T, PR = 16, and QS = 30. Determine and state the perimeter of PQRS.

27. Quadrilateral MATH and its image M'A'T'H' are graphed on the set of axes below

Describe a sequence of transformations that maps quadrilateral MATH onto quadrilateral M'A'T'H'.

28. Using a compass and straightedge, construct a regular hexagon inscribed in circle O. [Leave all construction marks.]

29. The coordinates of the endpoints of are A(2,3) and B(5,–1). Determine the length of A'B', the image of AB, after a dilation of centered at the origin.

30. In the diagram below of ABC and XYZ, a sequence of rigid motions maps ∠A onto ∠X, ∠C onto ∠Z, and AC onto XZ.

Determine and state whether BC ≅ YZ. Explain why.

31. Determine and state the coordinates of the center and the length of the radius of a circle whose equation is x

32. Triangle PQR has vertices P(-3,-1), Q(-1,7), and R(3,3), and points A and B are midpoints of PQ and RQ, respectively. Use coordinate geometry to prove that AB is parallel to PR and is half the length of PR.

[The use of the set of axes below is optional.]

33. In the diagram below of circle O, tangent EC is drawn to diameter AC. Chord BC is parallel to secant ADE, and chord AB is drawn.

Prove BC/CA = AB/EC

34. Keira has a square poster that she is framing and placing on her wall. The poster has a diagonal 58 cm long and fits exactly inside the frame. The width of the frame around the picture is 4 cm.

Determine and state the total area of the poster and frame to the nearest tenth of a square centimeter.

35. Isosceles trapezoid ABCD has bases DC and AB with nonparallel legs AD and BC. Segments AE, BE, CE, and DE are drawn in trapezoid ABCD such that ∠CDE ≅ ∠DCE, AE &prep; DE and BE &prep; CE.

Prove ADE ≅ BCE and prove AEB is an isosceles triangle.

36. A rectangular in-ground pool is modeled by the prism below. The inside of the pool is 16 feet wide and 35 feet long. The pool has a shallow end and a deep end, with a sloped floor connecting the two ends. Without water, the shallow end is 9 feet long and 4.5 feet deep, and the deep end of the pool is 12.5 feet long.

If the sloped floor has an angle of depression of 16.5 degrees, what is the depth of the pool at the deep end, to the nearest tenth of a foot?

Find the volume of the inside of the pool to the nearest cubic foot.

A garden hose is used to fill the pool. Water comes out of the hose at a rate of 10.5 gallons per minute. How much time, to the nearest hour, will it take to fill the pool 6 inches from the top? [1 ft

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