1. **State the problem:** We need to prove that parallelogram KLMN is a rhombus using the given statements and coordinates of vertices: \(M(1,1)\), \(N(3,5)\), \(L(5,3)\), and \(K(7,7)\). 2. **Recall the definition:** A rhombus is a parallelogram with all sides equal in length. 3. **Calculate the lengths of the sides:** - \(KM = \sqrt{(7-5)^2 + (7-3)^2} = \sqrt{2^2 + 4^2} = \sqrt{4 + 16} = \sqrt{20}\) - \(NL = \sqrt{(3-1)^2 + (5-1)^2} = \sqrt{2^2 + 4^2} = \sqrt{20}\) - \(LM = \sqrt{(5-1)^2 + (3-1)^2} = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20}\) - \(NK = \sqrt{(7-3)^2 + (7-5)^2} = \sqrt{4^2 + 2^2} = \sqrt{20}\) 4. **Check if all sides are equal:** All sides \(KM, NL, LM, NK\) have length \(\sqrt{20}\). 5. **Conclusion:** Since all sides are equal, parallelogram KLMN is a rhombus. 6. **Check the statements:** The statement "The slopes of LM and KN are both 1/2 and NK = ML = \sqrt{20}." matches our findings and proves the figure is a rhombus. **Final answer:** The correct statement is: "The slopes of LM and KN are both 1/2 and NK = ML = \sqrt{20}."