what are the statements and reasons?

Question

given: Quadrilateral ABCD = Quadrilateral EFGH; AD = CD

Prove: AD = GH what is the statement and reason?

Answer 1

Given: Quadrilateral ABCD = Quadrilateral EFGH; AD = CD

Since two consecutive sides of a quadrilateral are equal in length, the quadrilateral (ABCD) is both a parallelogram as well as more specifically a rhombus. Therefore, all four sides of quadrilateral ABCD are equal: AB = BC = CD = AD.

Since the two quadrilaterals are equal, this means that all four sides of quadrilateral EFGH are equal to each other: EF = FG = GH = EH.

Since the two quadrilateral are equal, and all corresponding sides are equal, this means that any pair of sides involving one side from each quadrilateral are equal. Therefore you can prove that AD = GH.