Question

In the straightedge and compass construction of the parallel line below, which of the following reasons can you use to prove that CD and EG are parallel?
A. ∠FCD ≅ ∠FDC by construction
B. ∠FEG≅ ∠FGE by construction
C. ∠FCD ≅ ∠GEC by construction
D. ∠FEG ≅ ∠FCD by construction

Answer 1

Answer:

D.

Step-by-step explanation:

Lines EG and CD are cut by transversal CF.

By construction, ∠FEG=∠FCD. These two angles are corresponding angles.

Since two corresponding angles are congruent, then lines EG and CD are parallel (by  converse of the corresponding angles postulate).

Converse of the Corresponding Angles Postulate: If the corresponding angles formed by two lines and a transversal are congruent, then lines are parallel.