Question

Determine if the triangles are congruent. If so, write a congruence statement.

Answer 1

Answer: There isn't enough information to say whether the triangles are congruent or not.

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Explanation:

Angles DCE and BCA are congruent because they are vertical angles.

I've marked these angles in blue.

In red, I've marked angles DEC and ABC. These are another congruent pair of angles because of the parallel lines DE and AB. Specifically, these are congruent alternate interior angles. The other pair of congruent alternate interior angles are the angles marked in green.

This shows that the triangles are similar. The question we want to answer is: are the triangles congruent?

The answer is unfortunately "cannot be determined". Why is this? Because of the placement of those "6"s. We would need to move one of the "6"s such that they must lay on the same line.

For instance, we would need to move the 6 on BC to AC. If we knew AC = 6, then we could conclude that the triangles are congruent by the ASA congruence theorem. However, we don't know any info about AC so we simply don't have enough information. The triangles may be congruent or they may not be.

If your teacher only gives you two options of "congruent" vs "not congruent", then I'd go for "not congruent". But to me, the best option is "not enough information".