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p^2+q^2=2(a^2+b^2)
where
p,q=diagonals of the parallelogram
a,b=sides of the parallelogram
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∙ 11y ago
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True or false the diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
What is the relationship between the number of sides of a polygon and the number of diagonals?
Number of diagonals = 1/2*(n2-3n) where n = the number of sides of the polygon.
Are diagonals of equal length in a parallelogram and rectangle?
the diagonal in a paralleogram is not equal but the diagonals in the rectangle are congruent this is because the opposite sides of a parallelogram and rectangle are same parallel to each other but the adjacent sides of a parallelogram is not perpendicular where as the adjacent sides of rectangle is perpendicular to each other.
What is the relationship between diagonals to the number of sides?
N(N-3)/2where N is the number of sides of a Polygon.
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.
What are the diagonals of a parallelogram?
The diagonals arenotthe sides. They're lines you draw from one angle of the parallelogram to the angle opposite it. So if you have parallelogram ABCD, your diagonals are AC and BD, because AB, BC, CD, and DA are all sides.
What has four sides and its opposite sides are parallel and the diagonals are not equal?
A parallelogram.
Does a parallelogram have adjacent sides equal?
A parallelogram has adjacent equal sides. Diagonals of a parallelogram bisect each other,Opposite sides of a parallelogram are parallel and will never intersect. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. Any line through the midpoint of a parallelogram bisects the area.
Name the best classification for a parallelogram with perpendicular diagonals?
The best classification for a parallelogram that has perpendicular diagonals is a rhombus. A rhombus has four sides that are congruent. The also diagonals bisect the vertex angles of this type of parallelogram.
True or false the diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
The diagonals are congruent but the quadrilateral has no right angles is it a parallelogram?
It can also be a kite. That has two congruent pairs of sides but unlike a parallelogram they are adjacent, not opposite. A parallelogram with congruent diagonals is a rectangle.
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
What is the relationship between the number of sides of a polygon and the number of diagonals?
Number of diagonals = 1/2*(n2-3n) where n = the number of sides of the polygon.
Are diagonals of equal length in a parallelogram and rectangle?
the diagonal in a paralleogram is not equal but the diagonals in the rectangle are congruent this is because the opposite sides of a parallelogram and rectangle are same parallel to each other but the adjacent sides of a parallelogram is not perpendicular where as the adjacent sides of rectangle is perpendicular to each other.
What quadrilaterals sides that are parallel to its opposite side and diagonals that are not perpendicular?
A parallelogram.
Are both diagonals of any parallelogram longer than the sides?
Yes.
If the diagonals of a quadrilateral bisect each other then what quadrilateral must be a parallelogram?
diagonals.
