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More Lessons for Regents Exam, More Geometry Lessons

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 #31 **

Parallel and perpendicular lines

Two lines are represented by the equations x + 2y = 4 and 4y − 2x = 12. Determine whether these lines are parallel, perpendicular, or neither. Justify your answer.**Geometry - June 2012 Regents - Q #32 **

Construction of an Angle Bisector

Using a compass and straightedge, construct the bisector of ∠CBA.

[Leave all construction marks.]**Geometry - June 2012 Regents - Q #33 **

Lateral Area of a Cylinder

The cylindrical tank shown in the diagram below is to be painted. The tank is open at the top, and the bottom does not need to be painted. Only the outside needs to be painted. Each can of paint covers 600 square feet. How many cans of paint must be purchased to complete the job?**Geometry - June 2012 Regents - Q #34 **

Locus of Points

On the set of axes below, graph the locus of points that are 4 units from the line x = 3 and the locus of points that are 5 units from the point (0,2). Label with an X all points that satisfy both conditions.

**Geometry - June 2012 Regents - Q #35**

Proof: Corresponding Parts of Congruent Triangles

Given: AD bisects BC at E.

AB ⊥ BC

DC ⊥ BC

Prove: AB is congruent to DC

**Geometry - June 2012 Regents - Q #36**

Transformations: Graphical Composition

The coordinates of trapezoid ABCD are A(−4,5), B(1,5), C(1,2), and D(−6,2). Trapezoid A"B"C"D" is the image after the composition r_{x-axis} ° r_{y = x} is performed on trapezoid ABCD. State the coordinates of trapezoid A"B"C"D".

[The use of the set of axes below is optional.]**Geometry - June 2012 Regents - Q #37**

Chords, Secants, and Tangents

In the diagram below of circle O, chords RT and QS intersect at M. Secant PTR and tangent PS are drawn to circle O. The length of RM is two more than the length of TM, QM = 2, SM = 12, and PT = 8. Find the length of RT. Find the length of PS.**Geometry - June 2012 Regents - Q #38**

Graphically Solving a System of Equations

On the set of axes below, solve the system of equations graphically and state the coordinates of all points in the solution.

y = (x − 2)^{2} − 3

2y + 16 = 4x.

More Lessons for Regents Exam, More Geometry Lessons

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.

Parallel and perpendicular lines

Two lines are represented by the equations x + 2y = 4 and 4y − 2x = 12. Determine whether these lines are parallel, perpendicular, or neither. Justify your answer.

Construction of an Angle Bisector

Using a compass and straightedge, construct the bisector of ∠CBA.

[Leave all construction marks.]

Lateral Area of a Cylinder

The cylindrical tank shown in the diagram below is to be painted. The tank is open at the top, and the bottom does not need to be painted. Only the outside needs to be painted. Each can of paint covers 600 square feet. How many cans of paint must be purchased to complete the job?

Locus of Points

On the set of axes below, graph the locus of points that are 4 units from the line x = 3 and the locus of points that are 5 units from the point (0,2). Label with an X all points that satisfy both conditions.

Proof: Corresponding Parts of Congruent Triangles

Given: AD bisects BC at E.

AB ⊥ BC

DC ⊥ BC

Prove: AB is congruent to DC

Transformations: Graphical Composition

The coordinates of trapezoid ABCD are A(−4,5), B(1,5), C(1,2), and D(−6,2). Trapezoid A"B"C"D" is the image after the composition r

[The use of the set of axes below is optional.]

Chords, Secants, and Tangents

In the diagram below of circle O, chords RT and QS intersect at M. Secant PTR and tangent PS are drawn to circle O. The length of RM is two more than the length of TM, QM = 2, SM = 12, and PT = 8. Find the length of RT. Find the length of PS.

Graphically Solving a System of Equations

On the set of axes below, solve the system of equations graphically and state the coordinates of all points in the solution.

y = (x − 2)

2y + 16 = 4x.

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