Question

proving the alternate interior angles converse exercise 3: given: ∠4≅∠5 prove: g || h statements 1.) ∠4≅∠5 2.) ∠1≅∠4 3.) ∠1≅∠5 4.) g || h reasons 1.) given 2.) 3.) 4.) corresponding angles converse

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. Since $\angle1$ and $\angle4$ are vertical angles, $\angle1\cong\angle4$.

Step2: Use the transitive property of congruence

Given $\angle4\cong\angle5$ and $\angle1\cong\angle4$, by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), we have $\angle1\cong\angle5$.

Step3: Apply corresponding - angles converse

If corresponding angles are congruent, then the lines are parallel. Since $\angle1$ and $\angle5$ are corresponding angles and $\angle1\cong\angle5$, we can conclude that $g\parallel h$.

Answer:

2.) Vertical angles are congruent.
3.) Transitive property of congruence.