Question

given: ℓ ∥ m; n ∥ p
prove: ∠2≅∠4
statements: reasons:
ℓ ∥ m
∠10 ≅ ∠14
n ∥ p given
∠2 ≅ ∠10
∠2 ≅ ∠14
transitive property
given
corresponding angles postulate

Explanation:

Step1: Identify given parallel lines

Given $\ell\parallel m$ and $n\parallel p$.

Step2: Use corresponding - angles postulate

Since $\ell\parallel m$, by the corresponding - angles postulate, $\angle2\cong\angle10$.

Step3: Use given congruent angles

We are given that $\angle10\cong\angle14$.

Step4: Apply transitive property

By the transitive property of congruence, if $\angle2\cong\angle10$ and $\angle10\cong\angle14$, then $\angle2\cong\angle14$.

Answer:

The reasons for the statements in the two - column proof are:

• For $\ell\parallel m$: Given
• For $\angle10\cong\angle14$: Given
• For $n\parallel p$: Given
• For $\angle2\cong\angle10$: Corresponding Angles Postulate
• For $\angle2\cong\angle14$: Transitive Property