Question

do the proof below. (e) 22. given: ∠e≅∠g, (overline{de}paralleloverline{fg}) prove: (overline{ef}paralleloverline{gh})

Explanation:

Step1: Use property of parallel lines

Since $\overline{DE}\parallel\overline{FG}$, then $\angle E=\angle EFG$ (alternate - interior angles).

Step2: Substitute given equal - angle

Given that $\angle E\cong\angle G$, so $\angle EFG=\angle G$ (by substitution).

Step3: Apply parallel - line criterion

If $\angle EFG=\angle G$, then $\overline{EF}\parallel\overline{GH}$ (alternate - interior angles are equal, so the lines are parallel).

Answer:

The proof is completed as above to show that $\overline{EF}\parallel\overline{GH}$.