Which quadrilateral is a parallelogram

III figure

Step-by-step explanation:

Parallelogram:It is a figure of four sides.The opposite sides of parallelogram are equal and parallel.

Properties of parallelogram:

1.Opposite angles are equal.

2.Opposite sides are equal and parallel.

3.Sum of interior angles on the same side is equal to 180 degrees.

4.Diagonals of parallelogram bisect to each other.

When sum of interior angles on the same side is equal to 180 degrees.Then, the sides are parallel.

When one pair of opposite sides is  parallel then, the quadrilateral is a parallelogram.

In I figure:

Sum of interior angles=

Sum of interior angles=

Side AC is not parallel to side BD.

Hence, it is not a  parallelogram .

In II figure:

Sum of interior angles=

Therefore, side AC is not parallel to side BD.

Hence, it is not a  parallelogram .

In III figure:

Sum of interior angles=

Therefore, side AC is  parallel to side BD.

Hence, quadrilateral ABCD is a parallelogram.

In IV figure:

Sum of interior angles=

Therefore, side AB is not parallel to side CD.

Hence, quadrilateral ABCD is not  a parallelogram.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt