• 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.