isn't it a rhombus ?
the ones that are like a slanted square ?
because there are no right angles but each diagonal bisects the corners.
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Such a shape cannot exist.
showing consecutive angles are congruent
Which quadrilateral or quadrilaterals cannot have two consecutive angles of 90° each
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.
Presuming our geometry is Euclidean, such a shape would be a rectangle, since all 4 angles would be right angles. If our geometry is hyperbolic, it would be possible to construct such a quadrilateral which is not a rectangle (and in fact, rectangles cannot exist in a hyperbolic geometry). I do not believe such a quadrilateral has any special name.
If it is a quadrilateral it cannot be "not a quadrilateral"!
It cannot. There is no way to draw a quadrilateral where 3 sides are congruent.
Such a shape cannot exist.
showing consecutive angles are congruent
A quadrilateral has 4 sides (quad), in a in a simple figure, the 4 sides can make at most 4 angles, so no quadrilateral has more (or less, in actuality) than 4 interior angles. if the figure is a complex quadrilateral, edges can cross to make up to 6 interior angles, but since the complex quadrilateral must then be reducible into 2 triangles, it cannot have 6 right angles.
A quadrilateral with no right angles can refer to most kites, most trapezoids, some parallelograms, and a few quadrilaterals that cannot be classified any more specifically.
Which quadrilateral or quadrilaterals cannot have two consecutive angles of 90° each
No. You can have a very "thin" quadrilateral that is completely in the top half of the circumscribing circle. Then the centre of the circle will be below and OUSIDE the quadrilateral. The diagonals of the quadrialteral will be INSIDE the quadrilateral while they are within the circle and so cannot pass through the centre.
A rhombus cannot be a cyclic quadrilateral because its opposite angles are not supplementary (unless it is a square). It cannot, therefore, have a radius.
Not possible... The internal angles of a quadrilateral always total 360. If you MUST have an angle of 90 degrees - the remaining angles must total 270. At least one of the remaining angles will always be obtuse.
A diagonal cannot be a side of a rectangle, and a side cannot be a diagonal.
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.