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Show that the diagonals of parallelogram divide it into four triangles of equal area?
Wiki User
∙ 13y ago
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.
Wiki User
∙ 13y ago
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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.
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 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
If ABCD is a parallelogram and the two diagonals are equal find the measure of angle ABC?
90 degrees - the parallelogram is a rectangle (or a square) if the diagonals are equal.
What are names of quadrilaterals which there diagonals do not bisect?
they are called parallelogram in which diagonals are equal
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
