Question

the proof below shows that corresponding angles are congruent when two parallel lines are cut by a transversal. statements 1. lines a and b are parallel cut by the transversal c. 2. ∠1≅∠4 3. ∠4≅∠5 4. if ∠1≅∠4 and ∠4≅∠5, then ∠1≅∠5 reasons given? ? transitive property what are the missing reasons for step 2 and step 3?

Explanation:

Step1: Analyze step 2

$\angle1\cong\angle4$ is given. Since lines $a$ and $b$ are parallel and cut by transversal $c$, $\angle1$ and $\angle4$ are corresponding - angles. The reason for step 2 is "Corresponding angles postulate".

Step2: Analyze step 3

$\angle4\cong\angle5$ is given. $\angle4$ and $\angle5$ are vertical angles. The reason for step 3 is "Vertical angles are congruent".

Answer:

Step 2 reason: Corresponding angles postulate
Step 3 reason: Vertical angles are congruent