The big picture
Eight ideas. This chapter starts from two facts. First, a straight angle is 180°. Second, a transversal cuts two lines. The lines are parallel exactly when corresponding angles are equal.
| Idea | Remember |
|---|---|
| Linear pair | Two angles that share a vertex and an arm, on opposite sides of it, with outer arms in a line, total 180°. Angles that total 180° are supplementary. |
| Converse | A claim turned around is a new claim. One drawing can end it. |
| Vertically opposite | Two linear pairs and one subtraction make the facing angles equal. |
| Parallel lines | Corresponding angles are equal. Alternate are equal. Co-interior total 180°. |
| Equal angles | Equal corresponding or alternate angles make the lines parallel. |
| Same line | Two lines parallel to a third line are parallel to each other. |
| Which fact | Start from parallel lines for angles. Start from equal angles for parallel lines. |
| When is it true | Always, only on parallel lines, or false as stated. |
The next chapter uses these ideas. It is about congruent triangles.