Geometry Postulates and Theorems textbook tutorials - definitions - constructions - postulates and theorems - internet activities and resources mathematical logic symmetry and similarity points, lines and planes parallel lines triangles quadrilaterals polygons circles 3-Dimensional Geometry If two parallel lines are intersected by a transversal then alternate interior angles are congruent. In a plane if two lines are both perpendicualar to a third line, then the two lines are parallel. If two parallel lines are intersected by a transversal then same-side interior angles are supplementary. If two lines are both parallel to a third line, then the two lines are parallel. If two lines are intersected by a tranversal and alternate interior angles are congruent, then the lines are parallel. If two parallel lines are intersected by a third line, then the lines of intersection are parallel. If two lines are intersected by a tranversal and same-side interior angles are supplementary then the lines are parallel. If two planes are both parallel to a third plane, then the two planes are parallel.