Given triangle abc whose sides are ab = 15 in. ac 25 in. and bc 30 in. from a point d on side ab, a line de is drawn to a point e on side ac such that angle ade is equal to angle abc. if the perimeter of triangle ade is 28 in. in find the lengths of line segments and ce?

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.