(5) Logical argument and constructions. The student uses constructions to validate conjectures about geometric figures. The student is expected to:
(A) 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, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools [such as compass and straightedge, paper folding, and dynamic geometric software] ;
(B) construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge;
(C) use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships; and
(D) verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.