Students know the definition of congruence and related notation, i.e., ≅. Students know that to prove two figures are congruent there must be a sequence of rigid motions that maps one figure onto the other.
Students know the basic properties of congruence are similar to the properties for all three rigid motions (translations, rotations, and reflections).
Students know that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines are equal. Students know that when these pairs of angles are equal, then lines are parallel.
Students know that corresponding angles of parallel lines are equal because of properties related to translation. Students know that alternate interior angles of parallel lines are equal because of properties related to rotation.
Students know the Angle Sum Theorem for triangles; the sum of the interior angles of a triangle is always 180°.
Students present informal arguments to draw conclusions about the angle sum of a triangle.
Students know a third informal proof of the angle sum theorem.
Students know how to find missing interior and exterior angle measures of triangles and present informal arguments to prove their answer is correct.
Students present informal arguments to draw conclusions about angles formed when parallel lines are cut by a transversal.