Question

given: rv bisects ∠srt. prove: ∠3 ≅ ∠1, ∠3 ≅ ∠2. proof statements 1. rv bisects ∠srt. 2. ∠3 ≅ ∠1. 3. ∠1 ≅ ∠2. 4. ∠3 ≅ ∠2. reasons

Explanation:

Step1: State the given information

Given: $\overrightarrow{RV}$ bisects $\angle SRT$.

Step2: Use the definition of an angle - bisector

By the definition of an angle - bisector, if a ray bisects an angle, it divides the angle into two congruent angles. So, $\angle 1\cong\angle 2$.

Step3: Given another angle congruence

Given: $\angle 3\cong\angle 1$.

Step4: Use the transitive property of congruence

Since $\angle 3\cong\angle 1$ and $\angle 1\cong\angle 2$, by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), $\angle 3\cong\angle 2$.

Answer:

Statements	Reasons
2. $\angle 1\cong\angle 2$	Definition of angle - bisector
3. $\angle 3\cong\angle 1$	Given
4. $\angle 3\cong\angle 2$	Transitive property of congruence