Question 1162375: given AB is parallel to DC, AB is congruent to DC, C is the midpoint of BE prove: AC is parallel to DE
Prove: triangle ABC is congruent to triangle to DCE
Answer by greenestamps(13200)   (Show Source):
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C is the midpoint of BE, so B, C, and E are collinear.
Then, because AB is parallel to CD, angles ABC and DCE are congruent.
Then, since AB is congruent to CD and BC is congruent to CE, triangles ABC and DCE are congruent by SAS.
Triangles ABC and DCE are congruent, and angles BCA and CED are congruent.
The sum of angles ABC, BCA, and CAB is 180 degrees; the sum of angles BCA, ACD, and DCA is 180 degrees.
Therefore, angles ACD and CDA are congruent.
And, therefore, AC and DE are parallel.
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