We know that angle 1 is congruent to angle 3 and that line A is parallel to line b because they are given. We see that __________ by the alternate exterior angles theorem. Therefore, angle 2 is congruent to angle 3 by the transitive property. So, we can conclude that lines e and f are parallel by the converse alternate exterior angles theorem. Which information is missing in the paragraph proof?
Answer
A
angle 1 is congruent to angle 4
B
angle 2 is congruent to angle 3
C
angle 2 is congruent to angle 4
D
angle 1 is congruent to angle 2
Explanation
Because lines A and b are parallel, the alternate exterior angles theorem gives ∠1 ≅ ∠2. Since ∠1 ≅ ∠3 is also given, the transitive property shows ∠2 ≅ ∠3. The missing information is “angle 1 is congruent to angle 2.”
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