Answer
1. Given
2. Definition
3. Angle Addition Postulate
4. Substitution
5. Substraction Property of Equality
6. Definition
Work Step by Step
1. $f$ and $g$ intersect.
2. Both $\angle ACD$ and $\angle BCE$ are straight angles.
3. $m\angle ACD = m\angle ACE +m\angle ECD = 180^{\circ}$
$m\angle BCE = m\angle ACE +m\angle ACB = 180^{\circ}$
4. $m\angle ACE +m\angle ECD = m\angle ACE +m\angle ACB$
5. $m\angle ECD = m\angle ACB$
6. If two angles have the same angle measure, they are congruent.
Therefore $\angle ECD$ and $\angle ACB$, which are vertical angles, are congruent.
