# Reasoning, Lines, and Transformations

G.1 The student will construct and judge the
validity of a logical argument consisting of a set of premises and a
conclusion.

This will include

a) identifying the converse, inverse, and contrapositive
of a conditional statement;

b) translating a short verbal argument into symbolic form;

c) using Venn diagrams to represent set relationships; and

d) using deductive reasoning.

Performance Assessments:

G.2 The student will use the relationships between
angles formed by two lines cut by a transversal to

a) determine whether two lines are parallel;

b) verify the parallelism, using algebraic and coordinate
methods as well as deductive proofs; and

c) solve real-world problems involving angles formed when
parallel lines are cut by a transversal.

Performance Assessments:

G.3 The student will use pictorial representations,
including computer software, constructions, and coordinate methods,

to solve
problems involving symmetry and transformation. This will include

a) investigating and using formulas for finding distance,
midpoint, and slope;

b) applying slope to verify and determine whether lines
are parallel or perpendicular;

c) investigating symmetry and determining whether a figure
is symmetric with respect to a line or a point; and

d) determining whether a figure has been translated,
reflected, rotated, or dilated, using coordinate methods.

Performance Assessments:

G.4 The student will construct and justify the
constructions of

a) a line segment congruent to a given line segment;

b) the perpendicular bisector of a line segment;

c) a perpendicular to a given line from a point not on the
line;

d) a perpendicular to a given line at a given point on the
line;

e) the bisector of a given angle,

f) an angle congruent to a given angle; and

g) a line parallel to a given line through a point not on
the given line.

Performance Assessments:

# Triangles

G.5 The student, given information concerning the
lengths of sides and/or measures of angles in triangles, will

a) order the sides by length, given the angle measures;

b) order the angles by degree measure, given the side
lengths;

c) determine whether a triangle exists; and

d) determine the range in which the length of the third
side must lie.

These concepts will be considered in the context of
real-world situations.

Performance Assessments:

G.6 The student, given information in the form of a
figure or statement, will prove two triangles are congruent, using algebraic
and coordinate methods as well as deductive proofs.

Performance Assessments:

G.7 The student, given information in the form of a
figure or statement, will prove two triangles are similar, using algebraic and
coordinate methods as well as deductive proofs.

Performance Assessments:

G.8 The student will solve real-world problems
involving right triangles by using the Pythagorean Theorem and its converse,

properties of special right triangles, and right triangle trigonometry.

Performance Assessments:

# Polygons and Circles

G.9 The student will verify characteristics of
quadrilaterals and use properties of quadrilaterals to solve real-world
problems.

Performance Assessments:

G.10 The student will solve real-world problems
involving angles of polygons.

Performance Assessments:

G.11 The student will use angles, arcs, chords,
tangents, and secants to

a) investigate, verify, and apply properties of circles;

b) solve real-world problems involving properties of
circles; and

c) find arc lengths and areas of sectors in circles.

Performance Assessments:

G.12 The student, given the coordinates of the center
of a circle and a point on the circle, will write the equation of the circle.

Performance Assessments:

# Three-Dimensional Figures

G.13 The student will use formulas for surface area
and volume of three-dimensional objects to solve real-world problems.

Performance Assessments:

G.14 The student will use similar geometric objects in
two- or three-dimensions to

a) compare ratios between side lengths, perimeters, areas,
and volumes;

b) determine how changes in one or more dimensions of an
object affect area and/or volume of the object;

c) determine how changes in area and/or volume of an
object affect one or more dimensions of the object; and

d) solve real-world problems about similar geometric
objects.

Performance Assessments: