Question

given: ∠1 and ∠2 are supplements, ∠3 and ∠4 are supplements, and ∠1 = ∠4. prove: ∠2 = ∠3. assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Recall definition of supplementary angles

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180$. Since $\angle3$ and $\angle4$ are supplementary, $m\angle3 + m\angle4 = 180$.

Step2: Use the given equality

Given that $\angle1=\angle4$, so $m\angle1=m\angle4$.

Step3: Substitute

Substitute $m\angle1$ for $m\angle4$ in the equation $m\angle3 + m\angle4 = 180$. We get $m\angle3 + m\angle1=180$.

Step4: Compare equations

We have $m\angle1 + m\angle2=180$ and $m\angle3 + m\angle1=180$. By the transitive - property of equality, $m\angle1 + m\angle2=m\angle3 + m\angle1$.

Step5: Subtract $m\angle1$ from both sides

Subtracting $m\angle1$ from both sides of the equation $m\angle1 + m\angle2=m\angle3 + m\angle1$, we get $m\angle2=m\angle3$, which implies $\angle2=\angle3$.

Answer:

$\angle2=\angle3$