Question

given: ∠1≅∠4, de∥bc. prove: ∠1≅∠2. statement: ∠1≅∠4, de∥bc, ∠2≅∠4, ∠2≅∠3. reason: given, alternate interior cs

Explanation:

Step1: Recall parallel - line property

Since $\overline{DE}\parallel\overline{BC}$, by the alternate - interior angles theorem, $\angle2\cong\angle4$.

Step2: Use given angle congruence

We are given that $\angle1\cong\angle4$.

Step3: Apply transitive property of congruence

If $\angle1\cong\angle4$ and $\angle2\cong\angle4$, then by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for angles), $\angle1\cong\angle2$.

Answer:

$\angle1\cong\angle2$ is proved using the alternate - interior angles theorem and the transitive property of congruence.