# Chapter 1 - Section 1.7 - The Formal Proof of a Theorem - Exercises - Page 56: 29

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.

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