Question

∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA by: the vertical angle theorem. the alternate interior angles theorem. the reflexive property. None of these choices are correct.

Answer 1

(B)the alternate interior angles theorem.

Explanation:

The diagram for the question is attached below:

In the diagram:

BC is parallel to AD; and

AB is parallel to DC.

Effectively, the shape is a parallelogram.

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

Therefore:

∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA by the alternate interior angles theorem.