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.

### June 2012 Geometry Regents Exam

Geometry - June 2012 Regents - Q #1

Transformations

Which transformation produces an image that is similar to, but not congruent to triangle ABC? Geometry - June 2012 Regents - Q #2

Negation

A student wrote the sentence “4 is an odd integer.” What is the negation of this sentence and the truth value of the negation? Geometry - June 2012 Regents - Q #3

Lines and Planes

As shown in the diagram below, computations.the line EF intersects planes P, Q, and R. If the line EF is perpendicular to planes P and R , which statement must be true?

Geometry - June 2012 Regents - Q #4

Trapezoid

In the diagram below, LATE is an isosceles trapezoid, with LE congruent to AT,

LA = 24, ET = 40, and AT = 10. Altitudes LF and AG are drawn. What is the length of LF? Geometry - June 2012 Regents - Q #5

Chords and Arcs

In the diagram below of circle O, diameter AB is parallel to chord CD. If the measure of arc CD = 70, what is the measure of the arc AC? Geometry - June 2012 Regents - Q #6

Subtraction Property

In the diagram below of line segment ABCD, AC is congruent to BD. Using this information, it can be proven that... Geometry - June 2012 Regents - Q #7

Volume of a Sphere

The diameter of a sphere is 15 inches. What is the volume of the sphere, to the nearest tenth of a cubic inch?

Geometry - June 2012 Regents - Q #8

Construction of Parallel Lines

The diagram below shows the construction of line.AB through point P parallel to line CD. Which theorem justifies this method of construction? Geometry - June 2012 Regents - Q #9

Parallelogram, Midpoint Formula

Parallelogram ABCD has coordinates A(1,5), B(6,3), C(3,−1), and D(−2,1). What are the coordinates of E, the intersection of diagonals

AC and BD? Geometry - June 2012 Regents - Q #10

Equation of a Circle

What is the equation of a circle whose center is 4 units above the origin in the coordinate plane and whose radius is 6? More Questions, Worked Solutions and Revision Resources for the Math Regents Examination

Transformations

Which transformation produces an image that is similar to, but not congruent to triangle ABC? Geometry - June 2012 Regents - Q #2

Negation

A student wrote the sentence “4 is an odd integer.” What is the negation of this sentence and the truth value of the negation? Geometry - June 2012 Regents - Q #3

Lines and Planes

As shown in the diagram below, computations.the line EF intersects planes P, Q, and R. If the line EF is perpendicular to planes P and R , which statement must be true?

Trapezoid

In the diagram below, LATE is an isosceles trapezoid, with LE congruent to AT,

LA = 24, ET = 40, and AT = 10. Altitudes LF and AG are drawn. What is the length of LF? Geometry - June 2012 Regents - Q #5

Chords and Arcs

In the diagram below of circle O, diameter AB is parallel to chord CD. If the measure of arc CD = 70, what is the measure of the arc AC? Geometry - June 2012 Regents - Q #6

Subtraction Property

In the diagram below of line segment ABCD, AC is congruent to BD. Using this information, it can be proven that... Geometry - June 2012 Regents - Q #7

Volume of a Sphere

The diameter of a sphere is 15 inches. What is the volume of the sphere, to the nearest tenth of a cubic inch?

Geometry - June 2012 Regents - Q #8

Construction of Parallel Lines

The diagram below shows the construction of line.AB through point P parallel to line CD. Which theorem justifies this method of construction? Geometry - June 2012 Regents - Q #9

Parallelogram, Midpoint Formula

Parallelogram ABCD has coordinates A(1,5), B(6,3), C(3,−1), and D(−2,1). What are the coordinates of E, the intersection of diagonals

AC and BD? Geometry - June 2012 Regents - Q #10

Equation of a Circle

What is the equation of a circle whose center is 4 units above the origin in the coordinate plane and whose radius is 6? More Questions, Worked Solutions and Revision Resources for the Math Regents Examination

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