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Show that the diagonals of parallelogram divide it into four triangles of equal area?
We know that diagonals of parallelogram bisect each other.
Therefore, O is the mid-point of AC and BD.
BO is the median in ΔABC. Therefore, it will divide it into two triangles of equal areas.
Area (ΔAOB) = Area (ΔBOC) ... (1)
In ΔBCD, CO is the median.
Area (ΔBOC) = Area (ΔCOD) ... (2)
Similarly, Area (ΔCOD) = Area (ΔAOD) ... (3)
From equations (1), (2), and (3), we obtain
Area (ΔAOB) = Area (ΔBOC) = Area (ΔCOD) = Area (ΔAOD)
Therefore, it is evident that the diagonals of a parallelogram divide it into four triangles of equal area.
What else can I help you with?
What are names of quadrilaterals which there diagonals do not bisect?
they are called parallelogram in which diagonals are equal
Are diagonals in a parallelogram equal in length?
the sides that are parallel of each other are equal. * * * * * True, but that was not the question! In general, the diagonals are not of equal length.
Is a rectangle a special case of parallelogram why?
yes it is it is a parallelogram of its angles is right or The two diagonals are equal in length
A quadrilateral with equal diagonals and no right angles?
An isosceles trapezoid will have diagonals of equal length but will never contain right angles by definition. A square and rectangle will have diagonals of equal length but will contain 4 right angles. A rhombus and any other parallelogram that does not contain right angles will not have diagonals of equal length.
Are the diagonals of a kite equal in length?
From Wikipedia: '...a kite, or deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite.' In other words, a kite consists of two isosceles triangles joined at the base. Beginning with a particular isosceles triangle, it will always be possible to construct from it one kite that has equal diagonals (given that the kite may be either convex or concave). Hence an infinite number of kites do have equal diagonals, but many do not. A notable example of a kite that does have equal diagonals is a square.
What is special about the diagonals of a parallelogram?
In a parallelogram, the diagonals bisect each other, meaning they cut each other exactly in half at their intersection point. Additionally, while the diagonals are not necessarily equal in length, they do divide the parallelogram into two congruent triangles. This property is fundamental in proving various characteristics of parallelograms and is essential in geometry.
Do the diagonals of a rhombus divide it into four triangles of equal areas?
Yes.
Do the diagonals of a rhombus divide it into four triangles of equal area?
Yes, they do.
What does each diagonal do to a parallelogram?
In a parallelogram, each diagonal divides the shape into two congruent triangles, ensuring that the areas of the resulting triangles are equal. The diagonals also bisect each other, meaning they intersect at their midpoints. Additionally, the diagonals can be used to determine the properties of the parallelogram, such as its symmetry and area.
What are facts about parallelogram?
Opposite sides are congruent Opposite sides are parallel Opposite angles are equal Consecutive angles are supplementary Diagonals bisect each other Diagonals form 2 equal triangles
The diagonals of a parallelogram are equal?
No, they are not.
Is diagonals of parallelogram equal?
No
Prove that if the diagonal of a parallelogram does not bisect the angles through the vertices to which the diagonal is drawn the parallelogram is not a rhombus?
Suppose that the parallelogram is a rhombus (a parallelogram with equal sides). If we draw the diagonals, isosceles triangles are formed (where the median is also an angle bisector and perpendicular to the base). Since the diagonals of a parallelogram bisect each other, and the diagonals don't bisect the vertex angles where they are drawn, then the parallelogram is not a rhombus.
The diagonals of a parallelogram must be what?
The diagonals of a parallelogram are congruent (equal in length) and bisect each other.
Is diagonals of a parallelogram are alwayssometimesnever congruent?
Sometimes as when the parallelogram is in the form of a rectangle then its diagonals are of equal lengths.
If a parallelogram is a rectangle then it's diagonals are what?
Its diagonals are equal in length
A parallelogram with intersecting diagonals is a?
A parallelogram with intersecting diagonals is a quadrilateral where opposite sides are parallel and equal in length, and the diagonals bisect each other. This means that the diagonals divide each other into two equal segments, which is a defining property of parallelograms. Additionally, the angles opposite each other are equal, and adjacent angles are supplementary. Thus, the intersecting diagonals further emphasize the symmetry and balance within the shape.
