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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 2014.

Geometry - January 2014 Regents - Q #1 - 5

- The midpoint of AB is M(4,2). If the coordinates of A are (6, -4), what are the coordinates of B?
- Which diagram shows the construction of a 45° angle?
- What are the coordinates of the center and the length of the radius of the circle whose equation is (x + 1)
^{2}+ (y - 5)^{2}= 16? - If distinct planes R and S are both perpendicular to line l, which statement must always be true?
- If triangle ABC and its image, triangle A’B’C’, are graphed on a set of axes, triangle ABC ≅ triangle A’B’C’ under each transformation except.

Geometry - January 2014 Regents - Q #6 - 10

6. A right rectangular prism is shown in the diagram below

Which pair of edges are not coplanar?

7. How many points in the coordinate plane are 3 units from the origin and also equidistant from both the x-axis and the y-axis?

8. As shown below, the medians of ABC intersect at D.

If the length of BE is 12, what is the length of B?

9. The solution of the system of equations y = x^{2} - 2 and y = x is

10. Line l passes through the point (5,3) and is parallel to line k whose equation is 5x + y = 6. An equation of line l is…

Geometry - January 2014 Regents - Q #11 - 15

11. In the diagram below of quadrilateral ABCD, E and F are points on AB and CD, respectively, BE ≅ DF, and AE ≅ CF.

Which conclusion can be proven?

12. In the diagram below, four pairs of triangles are shown.

Congruent corresponding parts are labeled in each pair.

Using only the information given in the diagrams, which pair of triangles can not be proven congruent?

13. In ABC shown below, L is the midpoint of BC , M is the midpoint of AB , and N is the midpoint of AC

If MN = 8, ML = 5, and NL = 6, the perimeter of trapezoid BMNC is .

14. In the diagram below, RCBT and ABC are shown with m∠A = 60

and m∠ABT = 125

What is m∠ACR?

15. Which equation represents circle O shown in the graph below?

Geometry - January 2014 Regents - Q #16 - 20

16. For which measures of the sides of triangle ABC is angle B the largest angle of the triangle?

Errata in the video

(4) 5/37 = 0.14

17. What is the measure of the largest exterior angle that any regular polygon can have?

18. As shown in the diagram below, a landscaper uses a cylindrical lawn roller on a lawn. The roller has a radius of 9 inches and a width of 42 inches

19. In the diagram below, AC and BC are tangent to circle O at Aand B, respectively, from external point C

20. What is the perimeter of a square whose diagonal is 3√2?

Geometry - January 2014 Regents - Q #21 - 25

21. The coordinates of point P are (7,1). What are the coordinates of the image of P after R90° about the origin?

22. Lines p and q are intersected by line r, as shown below

If m∠1 = 7x - 36 and m∠2 = 5x + 12, for which value of x would p || q?

23. What is the equation of the circle with its center at (-1,2) and that passes through the point (1,2)?

24. In the diagram below, diameter AB bisects chord CD at point E in circle F

If AE = 2 and FB = 17, then the length of CE is

25. Which quadrilateral does not always have congruent diagonals?

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