Russ P. answered • 12/20/14
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Inga,
Are your givens correct?
The only way that segment AD can be parallel to CD is if CD = AB, so segment CD lies on top of AB. As soon as there is any perpendicular distance between segments AB and CD, segment AD cannot be parallel to either AB or CD.
If AB & CD are congruent, then AD is also congruent on that line, and no triangles exist.
Am I somehow mis-interpreting your problem?
Russ P.
Inga,
I still don't get it based on your comment.
AD now crosses CB, so they can't be parallel. Draw it.
Are you trying to say that AC and BD must be parallel? They don't since parallel segments AB and CD are not constrained to have the same length. If they did, then you would have a rectangle whose opposite sides are parallel.
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12/24/14
Inga D.
12/24/14