A rectangle
Parallelogram and rectangle apex
Parallelogram and a rectangle
perpendicular
Is rectangle and any parallelogram not square or rhombus
No, a parallelogram does not have perpendicular sides by definition. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Perpendicular sides would form a right angle, which is a characteristic of rectangles, squares, and other types of quadrilaterals, but not parallelograms.
Parallelogram and rectangle apex
No
No. The only conditions to quality as a parallelogram is that it is a quadrilateral, and that opposite sides are parallel.
Parallelogram and a rectangle
If both pairs of opposite sides are parallel: A Rectangle, or a Square. If exactly one pair of opposite sides are parallel: An Isosceles Trapezoid. If it does not have parallel sides and one diagonal is the perpendicular bisector of the other: A Kite It is also possible that it does not have any parallel sides and neither diagonal is the perpendicular bisector of the other: A quadrilateral
Parallelogram and a rectangle
The Opposite Sides Parallel and Congruent Theorem states that if a quadrilateral has a pair of opposite sides that are parallel and congruent, then the quadrilateral is a parallelogram.
I would be seriously concerned if a quadrilateral had more than two pairs of opposite sides parallel! A quadrilateral with two pairs of opposite sides parallel is a parallelogram.
A rhombus is a type of quadrilateral where opposite sides are parallel, and adjacent sides are not. The opposite angles in a rhombus are also equal, and the diagonals bisect each other at right angles. Thus, while the sides are parallel (two pairs of parallel sides), they are not perpendicular to each other unless it is a special case of a rhombus, such as a square.
If it doesn't have parallel sides, it's just classified as a quadrilateral.
parallel
no, because parallel is opposite to perpendicular