Parallel lines and transversals
One line crosses two parallel lines. How many of the eight angles do you actually need to measure?
Where you are 4 inside
What this area is about
A transversal is a line that crosses two other lines, making eight angles at two crossings. When the two lines are parallel, any two of those eight angles are either equal or add to 180^\circ. Measure one angle and you know all eight.
How these fit together
The assumption. The parallel postulate says there is exactly one parallel through a point off a line. Every result below that starts from parallel lines leans on it.
Named pairs. Corresponding angles are equal when the lines are parallel. Alternate and same side angles gathers the rest: alternate interior and exterior angles are equal too, and same side interior angles are the odd one out, adding to 180^\circ. The same star chains these facts to fill in a whole figure.
Right angles and distance. Distance from a point to a line is measured along the perpendicular from the point. That star also holds the perpendicular transversal theorem: a transversal perpendicular to one of two parallel lines is perpendicular to the other, so one perpendicular drops square to both. Parallel lines stay the same distance apart.
A path through it
Take the postulate, then corresponding angles, then alternate and same side angles with their problems; each pair follows from corresponding angles with vertical angles or linear pairs. Distance from a point to a line comes last.
This area lets you prove lines are parallel, show the angles of a triangle add to 180^\circ, and work out the properties of a parallelogram.