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Which of the following is not a sufficient condition for concluding a quadrilateral is a parallelogram?
at least one pair of opposite sides is parallel
What else can I help you with?
Which description does not guarantee that a quadrilateral is a parallelogram?
A description that states a quadrilateral has one pair of opposite sides that are both equal and parallel does not guarantee that it is a parallelogram. While this condition is sufficient for proving that a quadrilateral is a parallelogram, it is not necessary; other configurations might exist where a quadrilateral meets this condition without being a parallelogram. Other descriptions, such as having both pairs of opposite sides equal or both pairs of opposite angles equal, would guarantee it is a parallelogram.
Condition which garanty that a quadrilateral is parallelogram?
The condition for being a parallelogram is that both pairs of opposite sides must be parallel.The condition for being a parallelogram is that both pairs of opposite sides must be parallel.The condition for being a parallelogram is that both pairs of opposite sides must be parallel.The condition for being a parallelogram is that both pairs of opposite sides must be parallel.
What is the relationship of the second sentence to the first in If a quadrilateral is a square then it is a parallelogram. 2. A quadrilateral is a square if and only if it is a parallelogram.?
The second sentence reiterates the relationship established in the first sentence but adds a stronger condition. The first sentence indicates that being a square implies being a parallelogram, while the second sentence specifies that the two properties are equivalent—meaning a quadrilateral is a square if and only if it is a parallelogram. This indicates a bidirectional relationship between the two concepts.
Which condition is sufficient to show that a quadrilateral is a trapezoid?
That it has 4 sides and a pair of parallel sides of different lengths
Is every square cyclic?
Yes. The sum of opposite angles is 180 degrees and that is a necessary and sufficient condition for a quadrilateral to be cyclic.
Can a quadrilateral abcd be aparallelogram if angle d plus angle b equals 180?
Yes, a quadrilateral ABCD can be a parallelogram if angle D plus angle B equals 180 degrees. In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their sum equals 180 degrees). Therefore, if angle D and angle B are supplementary, it is consistent with the properties of a parallelogram. Thus, the condition does not contradict the definition of a parallelogram.
Does a parallelogram have at least one pair of parallel lines?
Yes, a parallelogram has two pairs of parallel lines. By definition, a parallelogram is a quadrilateral with opposite sides that are both equal in length and parallel to each other. Therefore, it inherently possesses at least one pair of parallel sides, fulfilling the condition.
How are squares and rectangles paraellograms?
A parallelogram is any quadrilateral in which both sets of opposite sides are parallel, or will never intersect. Squares and rectangles (both quadrilaterals) satisfy that condition, and so would rhombus.
If the diagonals of a quadrilateral are perpendicular then the quadrilateral is a rhombus?
While it is true that if a quadrilateral has perpendicular diagonals, it can indicate that the shape is a rhombus, this condition alone is not sufficient for classification. Other quadrilaterals, such as kites, can also have perpendicular diagonals. Therefore, while perpendicular diagonals are a characteristic of rhombuses, they do not definitively determine that a quadrilateral is a rhombus without additional properties being met.
Can a trapezoid be a rectangle and why?
NO. A trapezoid cannot be a rectangle. If a parallelogram has one right angle then it is a rectangle. A trapezoid doesn't satisfy this condition because a trapezoid is a quadrilateral with exactly one parallel side which means that it doesn't have a right angle.
What condition would a parallelogram also be a rectangle?
A rectangle is a parallelogram where all internal angles are equal at 90°
Is a square a special type of parallelogram?
Yes, a square is a special type of parallelogram. Every square has two pairs of parallel sides, which is the condition for being a parallelogram.
