Given means that a step is true because if was “Given” in the problem statement.
Definition of congruent triangles: Congruent triangles are triangles whose corresponding sides and angles are congruent.
Definition of bisects a line segment: Saying that a point bisects a line segment means that the point divides the line segment into two congruent line segments.
Definition of bisects an angle: Saying that a line bisects an angle means that the line divides the angle into two congruent angles.
Definition of perpendicular lines: Perpendicular lines are lines that intersect and make adjacent angles congruent at their intersection.
Things are congruent to themselves means that anything is congruent to itself.
Side-angle-side means that if two triangles have two corresponding sides congruent, and the angles contained by these corresponding sides are congruent, then the triangles are congruent.
Angle-side-angle means that if two triangles have two corresponding angles congruent, and the sides contained by these corresponding angles are congruent, then the triangles are congruent.
Side-side-side means that if two triangles have all three corresponding sides congruent, then the triangles are congruent.