how does the fact that a parallelogram has rotational symmetry demonstrates that opposite side of a parallelogram are congruent ?

See below.

Step-by-step explanation:

It is known that a parallelogram has rotational symmetry, rotated 180 degrees about it's center point. Now by definition a parallelogram is a quadrilateral with two pairs of parallel sides, hence it's name. If you were to take a look at the attachment below, you might see the connection.

Rotational Symmetry will make it so that side AB corresponds to CD, respectively AD and CB. The sides will coincide with one another after a 180 degree rotation, so that AB = CD, and AD = CB. Hence, in the same parallelogram, opposite sides are congruent.

Proved!

the correct answer is the second option

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is