How to classify bolded triangles by its side and angles

Answer! if you don’t mind, can you explain

Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.

Which of these side lengths could form a triangle a) 2 cm , 2 cm , 4 cm b) 3 cm , 5 cm , 10 cm c) 3 cm , 4 cm , 5 cm d) 4 cm , 8 cm , 15 cm