At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Ok the statement right after the blank gives that "angles BCA and DAC are congruent by the same reasoning." These angles appear to me to be congruent according to the alternative interior angles theorem.
Where the parallel lines are BC and AD
after drawing the diagonal, you have 2 pairs of alternate angles in parallel lines... one pair has been identified, you need to identify the other pair |dw:1444072264928:dw| the equal angles are marked, the proof is Angle - Side -Angle...
Therefore the answer looks to be D, that angles BAC DCA are congruent by the same theorem where the parallel lines are taken to be CD and AB
way to go @PlasmaFuzer and @campbell_st !
Alternative Interior Angles Theorem gives that parallel lines cut by a transversal will yield 4 (interior) angles where the opposite angles are equal to one another as campbell shows.. here is something to get a little background: http://hotmath.com/hotmath_help/topics/alternate-interior-angles-theorem.html
the easy think to do in this question is sketch the diagram, do the construction, mark which is given to you and work from there... Open study is about helping understanding and not doing people's homework
@campbell_st Which is why I reasoned through it and further provided a link to get more understanding.... I find it quite difficult to use the drawing application on this site
@campbell_st Also I am still here in case anything isn't clear to provide further explanations if necessary.