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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 January 2015.

The following are questions for the past paper Regents High School Geometry January 2015 Exam (pdf).

Scroll down the page for the step by step solutions.

Geometry - January 2015 Regents - Questions and solutions 1 - 5

- What is the solution of the system of equations graphed below?
- What are the coordinates of the midpoint of the line segment with endpoints (2, -5) and (8,3)?
- As shown in the diagram below, when hexagon ABCDEF is reflected computations. over line m, the image is hexagon A’B’C’D’E’F’.

Under this transformation, which property is not preserved?

(1) area, (2) distance, (3) orientation, (4) angle measure

Geometry - January 2015 Regents - Questions and solutions 6 - 10

6. What are the truth values of the statement “Opposite angles of a trapezoid are always congruent” and its negation?

(1) The statement is true and its negation is true.

(2) The statement is true and its negation is false.

(3) The statement is false and its negation is true.

(4) The statement is false and its negation is false.

7. What is the length of a line segment whose endpoints have coordinates (5,3) and (1,6)?

Geometry - January 2015 Regents - Questions and solutions 11 - 15

11. A circle whose center has coordinates (-3,4) passes through the origin. What is the equation of the circle?

Geometry - January 2015 Regents - Questions and solutions 16 - 20

17. Given the statement, “If a number has exactly two factors, it is a prime number,” what is the contrapositive of this statement?

(1) If a number does not have exactly two factors, then it is not a prime number.

(2) If a number is not a prime number, then it does not have exactly two factors.

(3) If a number is a prime number, then it has exactly two factors.

(4) A number is a prime number if it has exactly two factors.

Geometry - January 2015 Regents - Questions and solutions 21 - 25

24. Triangle A’B’C’ is the image of ABC after a dilation of 2.

Which statement is true?

Geometry - January 2015 Regents - Questions and solutions 26 - 28

26. The bases of a prism are right trapezoids, as shown in the diagram below.

Which two edges do not lie in the same plane?

Geometry - January 2015 Regents - Questions and solutions 29 - 33

31. Determine and state the measure, in degrees, of an interior angle of a regular decagon.

32. Write an equation of a line that is parallel to the line whose equation is 3y x 6 and that passes through the point (-3,4).

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