Question

complete the two - column proof. given ∠1 ≅ ∠2 prove ∠1 ≅ ∠3 statements 1. ∠1 ≅ ∠2 2. ∠2 ≅ ∠3 3. blank reasons 1. given 2. blank 3. transitive property of angle congruence

Explanation:

Step1: Identify Vertical Angles

Vertical angles are congruent. $\angle 2$ and $\angle 3$ are vertical angles, so $\angle 2 \cong \angle 3$.

Step2: Apply Transitive Property

We know $\angle 1 \cong \angle 2$ (given) and $\angle 2 \cong \angle 3$ (vertical angles congruence). By the Transitive Property of Angle Congruence, if $\angle 1 \cong \angle 2$ and $\angle 2 \cong \angle 3$, then $\angle 1 \cong \angle 3$.

For the two - column proof:

Statements	Reasons
2. $\angle 2 \cong \angle 3$	2. Vertical Angles Theorem (Vertical angles are congruent)
3. $\angle 1 \cong \angle 3$	3. Transitive Property of Angle Congruence

Answer:

The completed two - column proof is as shown above, and we have proven that $\boldsymbol{\angle 1 \cong \angle 3}$ using the given information, the Vertical Angles Theorem, and the Transitive Property of Angle Congruence.