Consider the given information and the desired outcome of the proof.
Given:& ∠ 2 ≅ ∠ 3, & TVbisects ∠ UTW Prove:& Given
Let's do a two-column proof! Remember that this type of proof lists each statement on the left and its justification on the right. We will start with the given statement.
Statement1)& ∠ 2 ≅ ∠ 3, & TVbisects ∠ UTW Reason1)& Given
Let's now take a look at the given diagram.
If TV bisects ∠ UTW, by the definition of an angle bisector, we know that ∠ 1 and ∠ 2 are congruent.
Statement2)& ∠ 1 ≅ ∠ 2 Reason2)& Definition of angle bisector
Let's add this information to the diagram.
Since both ∠ 1 and ∠ 3 are congruent to ∠ 2, we can use the Transitive Property of Congruence to claim that ∠ 1 and ∠ 3 are congruent. This will give us our last statement.
Statement3)& ∠ 1 ≅ ∠ 3 Reason3)& Transitive Property of Congruence
Let's write this as a two-column proof.
