## 12.7 Chapter summary

- The sum of angles that are formed on a straight line is \(180^{\circ}\).
- Vertically opposite angles are always equal.
- If lines are parallel then:
- The corresponding angles are equal. (Reason: corresp \(\angle\)s; …//… )
- The alternate angles are equal. (Reason: alt \(\angle\)s; …//… )
- The co-interior angles are supplementary. (Reason: co-int \(\angle\)s; …//… ).

- Remember that you have to state which parallel lines you are using when you give the reasons above.

### Statements and abbreviations for reasons

- Angles on a straight line add up to \(180^{\circ}\) (\(\angle\)s on a str line)
- Vertically opposite angles are equal (vert opp \(\angle\)s)
- Angles around a point add up to \(360^{\circ}\) (\(\angle\)s around a pt)
- Corresponding angles of parallel lines are equal (corresp \(\angle\)s ; …//… )
- Alternate angles of parallel lines are equal (alt \(\angle\)s ; …//… )
- Co-interior angles between parallel lines add up to \(180^{\circ}\) (co-int \(\angle\)s ; …//… )
- The sum of the interior angles of a triangle add up to \(180^\circ\) (sum of \(\angle\)s in a \(\triangle\))
- The exterior angle of a triangle is equal to the sum of the interior opposite angles (exterior \(\angle\) of \(\triangle\))
- The interior angles of a quadrilateral add up to \(360^\circ\) (sum of \(\angle\)s in a quad)