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A quadrilateral whose opposite sides are parallel and opposite angles are congruent and that has four congruent sides is a?
this would be a rhombus. rhombuses are parallelograms (four-sided shapes with opposite sides parallel) that have all equal side lengths. squares are included as rhombuses.
How can you convince me that a rhombus is a parallelogram but a parallelogram is not a rhombus?
A parallelogram requires that opposite sides are parallel and of the same length; it is not a requirement that all four sides are of the same length. A rhombus requires that opposite sides are parallel and all four sides are of the same length. It is possible that a parallelogram can have all four sides of the same length; when it does it now fulfils the requirements of a rhombus, and so is a rhombus. Thus a rhombus is a type of parallelogram (all rhombuses are parallelograms), but there are parallelograms which are not rhombuses (those where there are two sides of one length (opposite and parallel) and the other two sides of a different length).
What do rhombuses and rectangles have in common?
Four sides, two pairs of parallel sides
What quadrilaterals have parallel sides and perpendicular diagonals?
They are squares and rhombuses
Why are rhombuses a parallelogram?
Because they have four sides that comprise two pairs of parallel sides.
