Why is every parallelogram is a quadrilateral but not every quadrilateral is a parallelogram?

Answer 1

Parallelogram:
a. 4 sides
b. 1 set of opposite sides is parallel
c. 1 more set of opposite sides being parallel

Quadrilateral:
a. 4 sides
b. 1 set of opposite sides is parallel

As can be seen above, the conditions for the Parallelogram is a super set of the Quadrilateral. A Quadrilateral needs one more condition to become a Parallelogram (another set of opposite sides being parallel).

Answer 2

Quadrilateral Parallelogram

Answer 3

Every Quadrilateral Is A Parallelogram

Answer 4

A problem arises because I don't know how you have defined quadrilateral and parallelogram, so I will use a funky answer.

A quadrilateral is a plane figure that has four sides that are line segments. (Or has vertices A, B, C, D where the line segments that form the sides are AB, BC, CD, DA and the sides intersect only at their end points. This isn't the best definition I ever gave but it will work.

A parallelogram is a quadrilateral with AB parallel CD and BC parallel to AD. That is, opposite sides are parallel

A trapezoid is a quadrilateral that is not a parallelogram; one pair of opposite sides are not parallel.

Every parallelogram has four sides and hence is a quadrilateral.

Answer 5

Because a parallelogram is a certain kind of quadrilateral, and there are all sorts of quadrilaterals, which means four sided. So square, rectangle, rhomboid, etc. are all quadrilateral and their sides are parallel. But not every four sided object has parallel opposite sides.

Answer 6

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RE:
Why is every parallelogram is a quadrilateral but not every quadrilateral is a parallelogram?

Answer 7

all parallelograms are quadrilaterals, because they all have 4 sides.

All quadrilaterals are not all parallelograms, because not all sides opposite to each other a parallel. Take the trapezoid for instance, all 2 sides are parallel, but the other to sides are not.

Answer 8

BY DEFINITION A QUADRILATERAL HAS FOUR SIDES WHICH CAN BE AN ANY ANGLE TO EACH OTHER AND CAN HAVE ANY SHAPE.
A PARALLELOGRAM BY DEFINITION IS A POLYGON WITH TWO SETS OF PARALLEL SIDES WHICH IN A TWO DIMENSIONAL PLANE CAN ONLY BE A FIGURE WITH FOUR SIDES WITH OPPOSITE SIDES PARALLEL
WHICH GIVES 1. A RECTANGLE IF CORNER ANGLES ARE RIGHT OR 90 DEGREE ANGLES 2. A SQUARE IF THE RECTANGLE HAS SIDES OF EQUAL LENGTH.
OR 3. A PLAIN PARALLELOGRAM IF IT CONTAINS NO RIGHT ANGLE.

Answer 9

Parallelogram by definition is a quadrilateral which has its opposite sides parallel.

That means SetOfParellalograms subset of SetOfQuadrilaterals.

Now to show that it suffices that there exists a quadrilateral which is not a parellalogram.
Take the vertices (0,0) (1,0) (2,1),(-1,1) [counter clockwise] of a quadrilateral. Now it is easy to verify that this is not a parellalogram. Take the slope of edge (1,0) (2,1) and (-1,1)(0,0) they are opposite sides but the slopes are +1 and -1 respectively.

For a parellalogram they need to be equal.

In this case the other two edges are parellal. We can as well make all pair of opposite edges non-parellall, by shifting the fourth vertex to (-1,2).

When one pair of opposite edges are parellal we call it a trapezoid.

Answer 10

A parallelogram is a 4-sided figure whose opposite sides are parallel. A quadrilateral is any 4-sided figure, and you can draw any number of 4-sided figures whose opposite sides are not parallel.