Question

drag each label to the correct location on the chart. given: ∠1≅∠2 prove: ∠3≅∠4 complete the flow - chart to prove ∠3≅∠4. ∠3≅∠4 ∠1≅∠2 ∠1≅∠3 ∠2≅∠4 vertical angles theorem ∠2≅∠3 transitive property of congruence given vertical angles theorem transitive property of congruence

Explanation:

Step1: Recall vertical - angles property

We know that $\angle1\cong\angle3$ and $\angle2\cong\angle4$ by the vertical - angles theorem.

Step2: Use given information and transitive property

Given $\angle1\cong\angle2$. Since $\angle1\cong\angle3$ and $\angle1\cong\angle2$, by the transitive property of congruence, $\angle2\cong\angle3$.

Step3: Use vertical - angles and transitive property again

Since $\angle2\cong\angle4$ (vertical - angles theorem) and $\angle2\cong\angle3$, by the transitive property of congruence, $\angle3\cong\angle4$.

Answer:

Drag $\angle1\cong\angle3$ to the box above $\angle2\cong\angle3$ (because of vertical - angles theorem). Drag $\angle2\cong\angle4$ to the box below $\angle2\cong\angle3$ (because of vertical - angles theorem). The proof is completed as $\angle3\cong\angle4$ is the final result we want to prove.