We understand that a rhombus is a parallelogram that has actually 1) equal sides and 2) diagonals that space perpendicular to every other. If, because that instance, we space a told the a figure is a parallelogram and that it has actually perpendicular diagonals we instantly know that it is a rhombus, identifier est, we understand all that is sides space equal.

You are watching: A parallelogram with 4 right angles

If we room told the a parallelogram has all sides equal, we recognize is a rhombus?

On the various other hand, we understand a rectangle is a parallel that satisfies 1) all angles equal come 90° and also 2) diagonals that room congruent (i.e. Same diagonals).

If we are told that a parallelogram has actually 4 best angles, or similarly, that a parallelogram has actually congruent diagonals, can we conclude instantly that that is a rectangle?

To amount up: four sides same in a parallelogram is tantamount to perpendicular diagonals and, likewise, 4 right angle in a parallelogram identical to congruent diagonals?

geometry rectangles square
edited Jun 12 "20 at 10:38

inquiry Oct 27 "19 at 11:35

Carlos NCarlos N
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You have to be clear through the definitions.Definition of parallel is a square whose opposite sides are parallel.Rhombus is characterized to be a quadrilateral with 4 equal sides.Now we deserve to prove the in a parallelogram,the the contrary sides have equal length.Now if 2 adjascent political parties of a parallelogram space equal,then it needs to be a rhombus together per the definition.Rectangle is characterized to it is in a parallel with among its angles a right angle.And square is characterized as a rectangle who adjoining sides are equal.You may find assist from the bookEuclidean geometry a an initial course-A Solomonovich.And please specify her doubts in the question.

edited Oct 27 "19 in ~ 12:23
answered Oct 27 "19 in ~ 12:02

Kishalay SarkarKishalay Sarkar
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