6.2.1 Properties of Special Parallelograms (continued)
A property of rectangles is used to find the length of half the diagonal of a quilt patch in this application example. It is given that the patch is a rectangle. The length of one side, EH , and the length of a diagonal, EG , are given. Here is a more direct proof than the one shown; try comparing them. By the properties of rectangles, the diagonals FH and EG are congruent. EG is given to be 20 in., so FH is 20 in. by the definition of congruent line segments. The diagonals of a rectangle bisect each other, so FJ = FH /2. Substitute 20 in. for FH to yield 10 in. for FJ .
Example 2 Using Properties of Rhombuses to Find Measures
This is a property of a rhombus. If a parallelogram is a rhombus, then its diagonals are perpendicular.
This is a property of a rhombus. If a parallelogram is a rhombus, then each of its diagonals bisects a pair of opposite angles.
This is a property of a rhombus. If a quadrilateral is a rhombus, then it is a parallelogram.
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