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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 June 2012.

Geometry - June 2012 Regents - Q #21

Diameter and Perpendicular Chord

21. In circle O shown below, diameter DB is perpendicular to chord AC at E. If DB = 34, AC = 30, and DE > BE, what is the length of BE?

Geometry - June 2012 Regents - Q #22

Parallelogram

In parallelogram ABCD shown below, diagonals AC and BD intersect at E. Which statement must be true?

Geometry - June 2012 Regents - Q #23

Graph of a circle

Which equation of a circle will have a graph that lies entirely in the first quadrant?

Geometry - June 2012 Regents - Q #24

Similar Triangles

In the diagram below, triangle ABC ∼ triangle RST. Which statement is not true?

Geometry - June 2012 Regents - Q #25

External Angle

In the diagram below of triangle ABC, BC is extended to D. If m∠A = x^{2} − 6x, m∠B = 2x − 3, and m∠ACD = 9x + 27, what is the value of x?

Geometry - June 2012 Regents - Q #26

Equation of a Parallel Line

An equation of the line that passes through (2,−1) and is parallel to the line 2y + 3x = 8 is

Geometry - June 2012 Regents - Q #27

Transformations: Glide Reflection

The graph below shows JT and its image, J’T’ after a transformation. Which transformation would map JT onto J’T'?

Geometry - June 2012 Regents - Q #28

Rhombus

Which reason could be used to prove that a parallelogram is a rhombus?

Geometry - June 2012 Regents - Q #29

Translation

Triangle TAP has coordinatesT(−1,4), A(2,4), and P(2,0).

On the set of axes below, graph and label triangle T’A’P’, the image of triangle TAP after the translation (x,y) → (x − 5, y − 1).

Geometry - June 2012 Regents - Q #30

Alternate Interior Angle

In the diagram below, l || m and QR ⊥ ST at R. If m∠1 = 63, find m∠2.

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