Mathematics

Mathematics

Problem

In quadrilateral ABCDABCD, the diagonal ACAC divides it into two congruent triangles, that is, △ABC≅△CDA\triangle ABC \cong \triangle CDA. a. (i) Prove that AB=CDAB = CD. b. (ii) Prove that AB∥CDAB \parallel CD. c. (iii) Hence show that ABCDABCD is a parallelogram. d. (iv) If AB=5 cmAB = 5\,\text{cm} and BC=3 cmBC = 3\,\text{cm}, find the perimeter of ABCDABCD."

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