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Rectangles, squares and rhombuses
1.
E is any point on side CD of square ABCD. DF is perpendicular to AE, meeting AE
at G, BC at F. Prove that DE = CF.
2.
Prove that a parallelogram is a rectangle if its diagonals are equal.
3.
Prove that a parallelogram is a rhombus if its diagonals are perpendicular.