ny-regents-exam-geometry-pt-i-august-2012

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In implementing the Geometry process and content performance indicators, it is expected that

students will identify and justify geometric relationships, formally and informally. For example,

students will begin with a definition of a figure and from that definition students will be expected

to develop a list of conjectured properties of the figure and to justify each conjecture informally

or with formal proof. Students will also be expected to list the assumptions that are needed in

order to justify each conjectured property and present their findings in an organized manner.

The intent of both the process and content performance indicators is to provide a variety of ways

for students to acquire and demonstrate mathematical reasoning ability when solving problems.

The variety of approaches to verification and proof is what gives curriculum developers and

Investigate/Explore - Students will be given situations in which they will be asked to look for

patterns or relationships between elements within the setting.

Discover - Students will make note of possible relationships of perpendicularity, parallelism,

congruence, and/or similarity after investigation/exploration.

Conjecture - Students will make an overall statement, thought to be true, about the new

discovery.

Reasoning - Students will engage in a process that leads to knowing something to be true or

false.

Argument - Students will communicate, in verbal or written form, the reasoning process that

leads to a conclusion. A valid argument is the end result of the conjecture/reasoning process.

Justify/Explain - Students will provide an argument for a mathematical conjecture. It may be an

intuitive argument or a set of examples that support the conjecture. The argument may include,

but is not limited to, a written paragraph, measurement using appropriate tools, the use of

dynamic software, or a written proof.

Proof - Students will present a valid argument, expressed in written form, justified by axioms,

definitions, and theorems using properties of perpendicularity, parallelism, congruence, and

similarity with polygons and circles.

Apply - Students will use a theorem or concept to solve a geometric problem.

Note: Two-dimensional geometric relationships are addressed

Relationships in the Informal and Formal Proofs band.

G.G.1 Know and apply that if a line is perpendicular to each of two

intersecting lines at their point of intersection, then the line is

perpendicular to the plane determined by them

G.G.2 Know and apply that through a given point there passes one

and only one plane perpendicular to a given line

G.G.3 Know and apply that through a given point there passes one

and only one line perpendicular to a given plane

G.G.4 Know and apply that two lines perpendicular to the same plane

are coplanar

G.G.5 Know and apply that two planes are perpendicular to each

other if and only if one plane contains a line perpendicular to

the second plane

Know and apply that if a line is perpendicular to a plane, then

any line perpendicular to the given line at its point of

intersection with the given plane is in the given plane

G.G.7 Know and apply that if a line is perpendicular to a plane, then

every plane containing the line is perpendicular to the given

plane

G.G.8 Know and apply that if a plane intersects two parallel planes,

then the intersection is two parallel lines

G.G.9 Know and apply that if two planes are perpendicular to the

same line, they are parallel

G.G.10 Know and apply that the lateral edges of a prism are congruent

and parallel

G.G.11 Know and apply that two prisms have equal volumes if their

bases have equal areas and their altitudes are equal

G.G.12 Know and apply that the volume of a prism is the product of

the area of the base and the altitude

G.G.13 Apply the properties of a regular pyramid, including:

o lateral edges are congruent

o lateral faces are congruent isosceles triangles

o volume of a pyramid equals one-third the product of the

area of the base and the altitude

G.G.14 Apply the properties of a cylinder, including:

o bases are congruent

o volume equals the product of the area of the base and

the altitude

o lateral area of a right circular cylinder equals the

product of an altitude and the circumference of the base

G.G.15 Apply the properties of a right circular cone, including:

o lateral area equals one-half the product of the slant

height and the circumference of its base

o volume is one-third the product of the area of its base

and its altitude

G.G.16 Apply the properties of a sphere, including:

o the intersection of a plane and a sphere is a circle

Investigate, justify, and apply the analytical representations for

translations, rotations about the origin of 90º and 180º,

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