Question

problem 18:
(first taught in lesson 27)
from this given statement, select the definition,
property, postulate, or theorem that justifies
the prove statement.
given: ∠3 and ∠4 are
supplementary.
prove: ℓ₁ || ℓ₂

Explanation:

Step1: Recall the theorem

If two lines are cut by a transversal and a pair of same - side interior angles are supplementary, then the two lines are parallel.

Step2: Identify the angles

In this case, \(\angle3\) and \(\angle4\) are same - side interior angles formed by the transversal intersecting lines \(l_1\) and \(l_2\).

Answer:

The theorem that justifies \(l_1\parallel l_2\) is "If two lines are cut by a transversal and a pair of same - side interior angles are supplementary, then the two lines are parallel."