August 22, 2013

This is a first year, high-school level course on Geometry (which is based on Euclid's elements). It revisits many of the basic geometrical concepts studied in earlier courses, but addresses them with more mathematical rigor. There is strong focus on proving theorems and results from basic postulates.

- Mathematics > General
- Mathematics > Geometry
- Mathematics > Problem Solving
- Mathematics > Trigonometry

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

translating a short verbal argument into symbolic form;

using Venn diagrams to represent set relationships; and

using deductive reasoning.

determine whether two lines are parallel;

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

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

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

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

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

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

a line segment congruent to a given line segment;

the perpendicular bisector of a line segment;

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

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

the bisector of a given angle;

an angle congruent to a given angle; and

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

order the sides by length, given the angle measures;

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

determine whether a triangle exists; and

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

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.

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.

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.

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

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

investigate, verify, and apply properties of circles;

solve real-world problems involving properties of circles; and

find arc lengths and areas of sectors in circles.

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