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Show that if diagonals of a quadrilateral bisects each other then it is a rhombus?
Wiki User
∙ 11y ago
This cannot be proven, because it is not generally true. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. And conversely, the diagonals of any parallelogram bisect each other. However not every parallelogram is a rhombus.
However, if the diagonals are perpendicular bisectors, then we have a rhombus.
Consider quadrilateral ABCD, with diagonals intersecting at X, where
AC and BD are perpendicular;
AX=XC;
BX=XD.
Then angles AXB, BXC, CXD, DXA are all right angles and are congruent.
By the ASA theorem, triangles AXB, BXC, CXD and DXA are all congruent.
This means that AB=BC=CD=DA.
Since the sides of the quadrilateral ABCD are congruent, it is a rhombus.
Wiki User
∙ 11y ago
Wiki User
∙ 7y agoABCD is a parallelogram => AB is congruent to DC and AD is congruent to BC.
Then, AD is congruent to AB => all four sides are congruent.
Thus ABCD is a parallelogram with four congruent sides. Therefore, by definition it is a rhombus.
Wiki User
∙ 6y agoIt is not possible to prove it because it is not true!
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What is the relationship between diagonals on a rhombus?
Not in general. The diagonals of a rectangle are equal length. A rhombus that is also a rectangle would be a square.
Does a square bisect each other?
The diagonals of any rhombus bisect each other. A square is a special kind of a rhombus.
Diagonals bisect each other at what angels for a rhombus?
They bisect each other at an angle of 90 degrees
Does the diagonal of a rectangle bisect each other?
Yes. The diagonals of any parallelogram bisect each other. A rectangle is a special case of a parallelogram.
In parallelogram the diagonals have the same midpoint?
Yes the diagonals of a parallelogram have the same midpoint since they bisect each other.
Which quadrilaterals have diagonals that bisects each other?
A quadrilateral whose diagonals bisect each other at right angles is a rhombus. each other at right angles at M. So AB = AD and by the first test above ABCD is a rhombus. 'If the diagonals of a parallelogram are perpendicular, then it is a rhombus
Do the diagonals of quadrilateral perpendiculary bisects each other?
Not necessarily.
Is it true if the diagonals of a quadrilateral bisects each other then the quaderateral is a parrallelogram?
Yes and the diagonals are not equal in length
A quadrilateral in which the diagonals bisect each other?
Square, Rhombus
Does a quadrilateral or a rectangle or a rhombus or square have diagonals bisect each other?
Not a quadrilateral. But "Yes" to a rhombus and a rectangle. And, since a square is a rectangle as well as a rhombus, a square as well.
What quadrilateral can have no right angles and diagonals bisect each other?
Parallelogram and rhombus.
What is the name of the quadrilateral that are perpendicular and bisect each other?
If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.
Which quadrilateral always has perpendicular diagonals?
A square, a rhombus and a kite have diagonals that intersect each other at right angles.
What special quadrilateral has diagonals that bisect each other but no right angles?
It is a rhombus or a kite
Why does it make sense knowing the diagonals of a quadrilateral are perpendicular is not sufficient to show the quadrilateral is a rhombus?
It makes sense because it is true. There are other quadrilaterals whose diagonals are perpendicular.
What is a quadrilateral with diagonals that bisect each other?
The diagonals of any parallelogram (square, rhombus, rectangle, rhomboid) bisect each other. The difference is the the diagonals are equal in length for a square and rectangle, and not equal for a rhombus or rhomboid (oblique diamond).
What type of figure must a quadrilateral be if its diagonals bisect each other?
A quadrilateral is a type of polygon that has four corners and sides. It is called a parallelogram (rectangle, square, or rhombus) when its diagonals bisect to each other.
