Derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines.
Determine an equation of a line parallel or perpendicular to a given line that passes through a given point.
Determine the image or pre-image of a given two-dimensional figure under a composition or rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane.
Identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse.
Verify that a conjecture is false using a counterexample.
Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles choosing from a variety of tools.
Construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, abd a line parallel to a given line through a point not on a line using a compass and a straightedge.
Use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships.
Verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.
Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and apply these relationships to solve problems.
Apply the definition of congruence, in terms of rigid transformations, to identify congruent figures and their corresponding sides and angles.
Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems.
Apply the formula for the area of regular polygons to solve problems using appropriate units of measure.