If two parallel lines are cut by a transversal — name all angle pairs

Label the angles at the intersection of $t$ with line $l$ as $\angle 1, \angle 2, \angle 3, \angle 4$ (going clockwise from the top-right). Similarly, label the angles at the intersection of $t$ with line $m$ as $\angle 5, \angle 6, \angle 7, \angle 8$.

          l
  \1 | 2/
   \3| 4/
    \|/
     t
    /|\
   / | \
  5\ | /8
   6\|/7
          m

More precisely, at line $l$: $\angle 1$ (top-right), $\angle 2$ (top-left), $\angle 3$ (bottom-left), $\angle 4$ (bottom-right). At line $m$: $\angle 5$ (top-right), $\angle 6$ (top-left), $\angle 7$ (bottom-left), $\angle 8$ (bottom-right).

Corresponding angles: Same position at each intersection — one is above the line, one is above the other parallel line, both on the same side of the transversal.

Pairs: $\angle 1$ and $\angle 5$; $\angle 2$ and $\angle 6$; $\angle 3$ and $\angle 7$; $\angle 4$ and $\angle 8$

Property: Equal (when lines are parallel)

Memory: “Same position, same side” → F-shape (when you trace the diagram, you can see F or backward-F shapes)

Alternate interior angles: Between the two parallel lines ($l$ and $m$), on opposite sides of the transversal.

Pairs: $\angle 3$ and $\angle 5$; $\angle 4$ and $\angle 6$

Property: Equal (when lines are parallel)

Memory: Z-shape or S-shape (the angles are at the “bends” of a Z or S)

Alternate exterior angles: Outside the two parallel lines, on opposite sides of the transversal.

Pairs: $\angle 1$ and $\angle 7$; $\angle 2$ and $\angle 8$

Property: Equal (when lines are parallel)

Co-interior angles (also called consecutive interior angles or allied angles): Between the two parallel lines, on the same side of the transversal.

Pairs: $\angle 3$ and $\angle 6$; $\angle 4$ and $\angle 5$

Property: Supplementary (add up to 180°)

Memory: C-shape or U-shape — the angles are inside the C. Since corresponding angles are equal and adjacent angles are supplementary, co-interior angles must add to 180°.