Answer and Step-by-step explanation:
A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles. A rectangle has all the properties of a parallelogram, plus the following: The diagonals are congruent.
Definition 1: A parallelogram is a four sided figure where the opposite sides are parallel.
Theorem 1: In a parallelogram, the opposite sides are of equal length.
Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram.
Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.
Theorem 4: If one pair of opposite sides in a four sided figure are both opposite and parallel, then the figure is a parallelogram.
Definition 2: A rectangle is a quadrilateral where all four angles are the same size.
Theorem 5: A rectangle is a parallelogram.
Theorem 6: A rectangle is a parallelogram if and only if the diagonals are the same length.
Definition 3: A rhombus is a quadrilateral where all four sides have the same length.
Theorem 7: A rhombus is a parallelogram.
Theorem 8: A quadrilateral is a rhombus if and only if the diagonals are perpendicular bisectors of each other.
Theorem 9: A quadrilateral is a rhombus if and only if the diagonals bisect all the vertex angles.
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