We know that a rhombus is a parallelogram that has 1) equal sides and 2) diagonals that are perpendicular to each other. If, for instance, we are a told that a figure is a parallelogram and that it has perpendicular diagonals we automatically know that it is a rhombus, id est, we know all its sides are equal.
If we are told that a parallelogram has all sides equal, we know is a rhombus?
On the other hand, we know a rectangle is a parallelogram that satisfies 1) all angles equal to 90° and 2) diagonals that are congruent (i.e. equal diagonals).
If we are told that a parallelogram has 4 right angles, or similarly, that a parallelogram has congruent diagonals, can we conclude immediately that it is a rectangle?
To sum up: four sides equal in a parallelogram is equivalent to perpendicular diagonals and, likewise, four right angles in a parallelogram equivalent to congruent diagonals?
Best Answer
You should be clear with the definitions.Definition of parallelogram is a quadrilateral whose opposite sides are parallel.Rhombus is defined to be a quadrilateral with 4 equal sides.Now we can prove that in a parallelogram,the opposite sides have equal length.Now if 2 adjascent sides of a parallelogram are equal,then it has to be a rhombus as per the definition.Rectangle is defined to be a parallelogram with one of its angles a right angle.And square is defined as a rectangle whose adjoining sides are equal.You may find help from the book Euclidean geometry a first course-A Solomonovich.And please specify your doubts in the question.