Answer:
a. given ∠1≅∠2, the converse of the corresponding angles theorem shows l║m.
Step-by-step explanation:
There are several things you need to know to be able to answer this question.
- corresponding angles where a transversal crosses (parallel) lines are angles that are in the same direction from the points of intersection. Here angles 1 and 2 are both "northwest" of the points of intersection, so are corresponding angles.
- the "corresponding angles theorem" tells you "if the lines are parallel, then corresponding angles at a transversal are congruent."
- the converse of a theorem "if A, then B" is "if B, then A". Here, the converse of the "corresponding angles theorem" is "if the corresponding angles at a transversal are congruent, then the lines are parallel."
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You are given ∠1 ≅ ∠2, so the hypothesis of the converse of the corresponding angles theorem is already true. The conclusion that the lines are parallel is what you are asked to prove. To prove that, you only need to identify the angles as being corresponding, and invoke the theorem. The logic matches answer choice A.
∠1≅∠2 is given. The diagram shows ∠1 and ∠2 are corresponding angles, so by the converse of the Corresponding Angles Theorem, l║m.
