- D is the midpoint of AB, E is the midpoint of BC
Answer: A. Given
I left off DB||FC because that's not given. But we can construct it.
Construct line through C parallel to AB. Extend DE to intersect and call the meet F.
- DB || FC
By Construction
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- Angle B congruent to angle FCE
Answer: D. Alternate Interior Angles
We have transversal BC across parallel lines AB and CF, so we get congruent angles ABC and FCB aka FCE
- angle BED congruent to angle CEF
Answer: H. Vertical angles are congruent
When we get lines meeting like this we get the usual congruent and supplementary angles.
- Triangle BED congruent to Triangle CEF
Answer: F. Angle Side Angle
We have BE=CE, DBE=FCE, BED=CEF
- DE congruent to FE and DB congruent to FC
Answer: C. CPTCTF
Corresponding parts ...
- AD congruent to DB and DB congruent to FC therefore AD congruent to FC
Answer: E. Transitive Property of Congruent
Things congruent to the same thing are congruent
- ADFC is a parallelogram
Answer: G. AD and FC are congruent and parallel
Presumably this is a theorem we have already established.
- DE || AD
Answer: B. Definition of a parallelogram
