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A quadrilateral with equal diagonals that are also perpendicular?
Wiki User
∙ 13y ago
A square
Wiki User
∙ 13y ago
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What quadrilateral does NOT always have perpendicular diagonals?
rectangleA trapezoid will also suffice.
What are all of the quadrilaterals with perpendicular diagonals?
If a quadrilaterl has a perpendicular diagonas it is a roumbus, also kite has perperndicular diagonals
If one diagonal of a quadrilateral bisects the other then the quadrilateral isa parallelogram?
not necessarily. because the diagonals of a trapezium also bisect each other and it is not a parallelogram. in order for the quadrilateral to become a parallelogram, the opposite angles of it must be equal, and the opposite sides must be equal too. the angles formed by the two diagonals( four in number) also must be equal if they are opposite angles not alternating angles.that's it pal
Why are the diagonals of a square perpendicular bisectors of each other?
You could prove this by congruent triangles, but here are two simpler arguments: --------------- Since a square is a rhombus, and the diagonals of a rhombus are perpendicular bisectors of each other, then the diagonals of a square must be perpendicular bisectors of each other -------------------- A square has four-fold rotational symmetry - as you rotate it around the point where the diagonals cross, there are four positions in which it looks the same. This means that the four angles at the centre must be equal. They will each measure 360/4 = 90 degrees, so the diagonals are perpendicular. Also. the four segments joining the centre to a vertex are all equal, so the diagonals bisect each other.
A quadrilateral having both diagonals congruent is a?
If both pairs of opposite sides are parallel: A Rectangle, or a Square. If exactly one pair of opposite sides are parallel: An Isosceles Trapezoid. If it does not have parallel sides and one diagonal is the perpendicular bisector of the other: A Kite It is also possible that it does not have any parallel sides and neither diagonal is the perpendicular bisector of the other: A quadrilateral
What quadrilateral does not have perpendicular diagonals?
rectangleA trapezoid will also suffice.
If a quadrilateral has the property that the diagonals are perpendicular and at least one of them is then the quadrilateral is a kite?
It can be but a square and a rhombus diagonals are also perpendicular and therefore intersect at 90 degrees and they too are both quadrilaterals.
What quadrilateral does NOT always have perpendicular diagonals?
rectangleA trapezoid will also suffice.
Is a quadrilateral with congruent and perpendicular diagonals a square or a rhombus?
It could be a square, but consider the following congruent & perpendicular 'diagonals of a quadrilateral (you will have to connect the endpoints of the diagonals, yourself, as it cannot be drawn in text): . _|___ . | . | . | If the two diagonals, also bisect each other, then it's a square, otherwise it is not.
What is a quadrilateral with equal sides that are also perpendicular?
square
Are the diagonals of rectangles perpendicular?
In general they are not; they are perpendicular only if the rectangle is also a sqare. However, the diagonals of a retangle have another attribute: They are of equal length and bisect each other.
Does a parallelogram have perpendicular diagonals?
No, not necessarily. It would have to also be a square or a kite in order to have perpendicular diagonals.
Maximum no of diagonals does quadrilateral have?
A quadrilateral has two and only two diagonals. That's the maximum and also the minimum. If it has more or fewer than two diagonals, it's not a quadrilateral.
What are all of the quadrilaterals with perpendicular diagonals?
If a quadrilaterl has a perpendicular diagonas it is a roumbus, also kite has perperndicular diagonals
If one diagonal of a quadrilateral bisects the other then the quadrilateral isa parallelogram?
not necessarily. because the diagonals of a trapezium also bisect each other and it is not a parallelogram. in order for the quadrilateral to become a parallelogram, the opposite angles of it must be equal, and the opposite sides must be equal too. the angles formed by the two diagonals( four in number) also must be equal if they are opposite angles not alternating angles.that's it pal
Is a parallelogram's diagonals perpendicular?
If the parallelogram happens to also be a rhombus (i.e. has all sides equal in length) then yes, otherwise no.
Why are the diagonals of a square perpendicular bisectors of each other?
You could prove this by congruent triangles, but here are two simpler arguments: --------------- Since a square is a rhombus, and the diagonals of a rhombus are perpendicular bisectors of each other, then the diagonals of a square must be perpendicular bisectors of each other -------------------- A square has four-fold rotational symmetry - as you rotate it around the point where the diagonals cross, there are four positions in which it looks the same. This means that the four angles at the centre must be equal. They will each measure 360/4 = 90 degrees, so the diagonals are perpendicular. Also. the four segments joining the centre to a vertex are all equal, so the diagonals bisect each other.
