If the quadrilateral is convex, the answer is yes and there are several cases to consider.
If the quadrilateral is NOT convex, I am not sure of the answer.
I can prove the answer in the case of a convex quadrilateral, but my proof requires use of the law of sines and it is divided into several cases. When you draw a figure you will see that there are several cases depending on the length of the diagonal, which is determined by the length of the sides and the measures of the angles.
The law of sines allows you to prove that there are 2 congruent triangles to consider and then you will have proof that the given sides are, in fact, parallel.
Start by drawing a figure; then work out the relationship of the angles and then use the law of sines.
11/15/2022 3:34 PM
After some more thinking and looking at the figures, I found the piece of information I needed to do the proof without the law of sines. If perpendiculars are drawn from the vertices which do not contain the equal angles to the respective equal sides, there will be two congruent right triangles which will allow the conclusion to be drawn.
