Answer: Choice E) Insufficient information to prove congruence.
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Explanation:
We're given that AB = DC and BE = CE. This means we have two pairs of congruent sides and we could use SAS if we know that angle ABE = angle DCE. However, we don't know this information.
While we do know that angle AEB = angle DEC (vertical angle theorem), this is not enough information. Recall that SSA is not a valid congruence theorem. The angles in question are not between the sides mentioned in the previous paragraph.
Therefore, we don't have enough information to prove the triangles congruent.
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Side notes:
- We can't use SSS because we don't have info about three pairs of sides. We only have info about two pairs of sides.
- We can't use ASA because we only have info about one pair of angles.
- We can't use HL because this only applies to right triangles.
