6.2.1 Properties of Special Parallelograms Key Objectives • Prove and apply properties of rectangles, rhombuses, and squares. • Use properties of rectangles, rhombuses, and squares to solve problems. Key Terms • A rectangle is a quadrilateral with four right angles. • A rhombus is a quadrilateral with four congruent sides. • A square is a quadrilateral with four right angles and four congruent sides.
Theorems, Postulates, Corollaries, and Properties • Theorem If a quadrilateral is a rectangle, then it is a parallelogram. • Theorem If a parallelogram is a rectangle, then its diagonals are congruent. • Theorem If a quadrilateral is a rhombus, then it is a parallelogram. • Theorem If a parallelogram is a rhombus, then its diagonals are perpendicular. • Theorem If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. Example 1 Craft Application This is a property of a rectangle. If a quadrilateral is a rectangle, then it is a parallelogram.
This is a property of a rectangle. If a parallelogram is a rectangle, then its diagonals are congruent.
A property of rectangles is used to find the length of the sides 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. By the properties of rectangles, opposite sides are congruent, so FG ≅ EH . EH is given as 12 in., so by the definition of congruent line segments, FG is also 12 in.
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