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More Lessons for the Regents High School Exam

More Lessons for Geometry

High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry Regents High School Examination January 2013.

Geometry - January 2013 Regents - Q #1 - 5

- If triangle MNP is congruent to triangle VWX and PM is the shortest side of triangle MNP, what is the shortest side of triangle VWX?
- In circle O shown in the diagram below, chords AB and CD are parallel. If mAB = 104 and mCD = 168, what is mBD ?
- As shown in the diagram below, CD is a median of ABC. Which statement is always true?
- In the diagram below, under which transformation is triangle A’B’C’ the image of triangle ABC?
- Line segment AB is a diameter of circle O whose center has coordinates (6,8). What are the coordinates of point B if the coordinates of point A are (4,2)?

Geometry - January 2013 Regents - Q #6 - 10

6. Plane A and plane B are two distinct planes that are both perpendicular to line ?. Which statement about planes A and B is true?

7. Triangle ABC is similar to triangle DEF. The lengths of the sides of triangle ABC are 5, 8, and 11. What is the length of the shortest side of triangle DEF if its perimeter is 60?

8. In the diagram below of right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD = 3 and DB = 12, what is the length of altitude CD?

9. The diagram below shows the construction of an equilateral triangle. Which statement justifies this construction?

10. What is the slope of the line perpendicular to the line represented by the equation 2x + 4y = 12?

Geometry - January 2013 Regents - Q #11 - 15

11. Triangle ABC is shown in the diagram below. If DE joins the midpoints of ADC and AEB which statement is not true?

12. The equations x^{2} + y^{2} = 25 and y = 5 are graphed on a set of axes. What is the solution of this system?

13. Square ABCD has vertices A(-2,-3), B(4,-1), C(2,5), and D(-4,3). What is the length of a side of the square?

14. The diagram below shows triangle ABD, with a ray ABC, BE ⊥ AD and ∠ EBD is congruent to ∠ CBD. If m ∠ ABE = 52, what is m ∠ D?

15. As shown in the diagram below, FD and CB intersect at point A and ET is perpendicular to both FD and CB at A. Which statement is not true?

Geometry - January 2013 Regents - Q #16 - 25

16. Which set of numbers could not represent the lengths of the sides of a right triangle?

17. How many points are 5 units from a line and also equidistant from two points on the line?

18. The equation of a circle is (x - 2)^{2} + (y + 5)^{2} = 32. What are the coordinates of the center of this circle and the length of its radius?

19. The equation of a line is y = 2/3x + 5. What is an equation of the line that is perpendicular to the given line and that passes through the point (4,2)?

20. Consider the relationship between the two statements.

21. In the diagram of trapezoid ABCD below, AB || DC, AD = BC, m ∠ A = 4x + 20, and m ∠ C = 3x - 15.

22. In circle R shown below, diameter DE is perpendicular to chord ST at point L. Which statement is not always true?

23. Which equation represents circle A shown in the diagram below?

24. Which equation represents a line that is parallel to the line whose equation is 3x - 2y = 7?

25. In the diagram below of circle O, PAC and PBD are secants. If mCD = 70 and mAB = 20, what is the degree measure of ?P?

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