Question

problem 12: (first taught in lesson 26)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: ∠dge ≅ ∠feg
prove: dg || ef

Explanation:

The given angles ∠DGE and ∠FEG are alternate - interior angles. By the Alternate - Interior Angles Converse Theorem, if two lines are cut by a transversal and the alternate - interior angles are congruent, then the two lines are parallel. Here, since ∠DGE≅∠FEG, we can conclude that DG∥EF.

Answer:

The Alternate - Interior Angles Converse Theorem