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Show that if diagonals of a quadrilateral bisects each other then it is a rhombus?
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.
What else can I help you with?
What is the mathematical way to call a diamond?
In mathematical terms, a diamond shape is often referred to as a "rhombus." A rhombus is a type of quadrilateral where all four sides are of equal length, and opposite angles are equal. Additionally, the diagonals of a rhombus bisect each other at right angles.
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.
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
If the diagonals of a quadrilateral are perpendicular then the quadrilateral is a rhombus?
While it is true that if a quadrilateral has perpendicular diagonals, it can indicate that the shape is a rhombus, this condition alone is not sufficient for classification. Other quadrilaterals, such as kites, can also have perpendicular diagonals. Therefore, while perpendicular diagonals are a characteristic of rhombuses, they do not definitively determine that a quadrilateral is a rhombus without additional properties being met.
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.
In which quadrilateral are the diagonals always congruent?
The diagonals of a rhombus are always congruent. A rhombus is a quadrilateral with all sides of equal length. Due to its symmetry, the diagonals of a rhombus bisect each other at right angles, and they are always of the same length. This property distinguishes a rhombus from other quadrilaterals like rectangles or parallelograms.
