Verification and Proof
Students will recognize verification and proof as fundamental aspects of mathematical reasoning. Students will integrate
and apply inductive and deductive reasoning skills to make, test, and evaluate mathematical statements. This applies equally
through simple mathematical calculations, in geometric applications, and more abstract statistical and algebraic processes.
Students will use logical reasoning to analyze an argument and to determine whether conclusions are valid.
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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.
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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.
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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.
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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.
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The student will verify basic trigonometric identities and make substitutions, using the basic identities.
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