Want this question answered?
Sure they are. They fulfill all the requirements of a trapezoid. To be precise, it depends how exactly you choose to define a trapezoid. If you define a trapezoid as a quadrilateral which has AT LEAST one pair of parallel sides, then that applies to rectangles as well. If you want it to have EXACTLY one pair of parallel sides, then a rectangle is not a trapezoid, since it has two pairs of parallel sides.
define the following write the units and formula
Elliptical geometry is like Euclidean geometry except that the "fifth postulate" is denied. Elliptical geometry postulates that no two lines are parallel.One example: define a point as any line through the origin. Define a line as any plane through the origin. In this system, the first four postulates of Euclidean geometry hold; through two points, there is exactly one line that contains them (i.e.: given two lines through the origin, there is one plane that contains them) and so on. However, it is nottrue that given a line and a point not on the line that there is a parallel line through the point (that is, given a plane through the origin, and a line through the origin, not on the plane, there is no other plane through the origin that is parallel to the given plane).
Trapezoids are not considered parallelograms because parallelograms have 2 pairs of parallel sides, whereas trapezoids have only one. Some definitions of trapezoid say "at least one pair of parallel sides" in which case, some trapezoids would be parallelograms (the ones that have 2 pairs of parallel sides), but most textbooks in the US now define trapezoids as "exactly one pair of parallel sides."
First of all, a trapezoid is not always a parallelogram. Did you mean the reverse: "Why is a parallelogram also a trapezoid"? If so, this depends upon your definition of a trapezoid and parallelogram. Some people define a trapezoid as a quadrilateral with exactly one pair of parallel sides, and a parallelogram as a quadrilateral with exactly two pairs of parallel sides. According to these definitions, a trapezoid can *NEVER* be a parallelogram, so your question is meaningless. However, others might define a trapezoid as a quadrilateral with one *or two* pairs of parallel sides. If you use this definition, then all parallelograms are also trapezoids, much in the same manner that all squares are also rectangles.
Playfair Axiom
Sure they are. They fulfill all the requirements of a trapezoid. To be precise, it depends how exactly you choose to define a trapezoid. If you define a trapezoid as a quadrilateral which has AT LEAST one pair of parallel sides, then that applies to rectangles as well. If you want it to have EXACTLY one pair of parallel sides, then a rectangle is not a trapezoid, since it has two pairs of parallel sides.
Some people define trapezoids as having at least one pair of parallel sides. By this definition, all parallelograms are trapezoids, though not all trapezoids are parallelograms.Some people define trapezoids as having exactly one pair of parallel sides. By this definition, the terms "trapezoid" and "parallelogram" are mutually exclusive.
define the following write the units and formula
START: Define the problem (I am not asking you here. I mean: DEFINE exactly what the problem is. Write it down or think it through WHAT the problem consists of, in as much detail as possible)
Elliptical geometry is like Euclidean geometry except that the "fifth postulate" is denied. Elliptical geometry postulates that no two lines are parallel.One example: define a point as any line through the origin. Define a line as any plane through the origin. In this system, the first four postulates of Euclidean geometry hold; through two points, there is exactly one line that contains them (i.e.: given two lines through the origin, there is one plane that contains them) and so on. However, it is nottrue that given a line and a point not on the line that there is a parallel line through the point (that is, given a plane through the origin, and a line through the origin, not on the plane, there is no other plane through the origin that is parallel to the given plane).
Line, plane
Depends on what you define the "base" as. A trapezoid always has two parallel bases, by definition. Hope this helps ! :)
Trapezoids are not considered parallelograms because parallelograms have 2 pairs of parallel sides, whereas trapezoids have only one. Some definitions of trapezoid say "at least one pair of parallel sides" in which case, some trapezoids would be parallelograms (the ones that have 2 pairs of parallel sides), but most textbooks in the US now define trapezoids as "exactly one pair of parallel sides."
exactly!:)
First of all, a trapezoid is not always a parallelogram. Did you mean the reverse: "Why is a parallelogram also a trapezoid"? If so, this depends upon your definition of a trapezoid and parallelogram. Some people define a trapezoid as a quadrilateral with exactly one pair of parallel sides, and a parallelogram as a quadrilateral with exactly two pairs of parallel sides. According to these definitions, a trapezoid can *NEVER* be a parallelogram, so your question is meaningless. However, others might define a trapezoid as a quadrilateral with one *or two* pairs of parallel sides. If you use this definition, then all parallelograms are also trapezoids, much in the same manner that all squares are also rectangles.
for what