Which of the following are not sufficient to prove that a quadrilateral is a parallelogram?

i. two pairs of opposite angles congruent.
ii. a pair of adjacent angles are supplementary.
iii. both pairs of opposite sides are congruent.
iv. a pair of opposite angles congruent and a pair of opposite sides congruent.
v. both pairs of opposite sides are parallel.
vi. a pair of opposite sides parallel and the other pair of opposite sides congruent.
vii. one pair of opposite sides are both parallel and congruent.
viii. the diagonals bisect each other.

Answer with explanation:

We can prove that a quadrilateral is a parallelogram , if

I. Two pairs of opposite angles congruent.

Consider, a Quadrilateral ABCD, in which , ∠A=∠C,and ∠B=∠D.

Now, ∠A+∠B+∠C+∠D=360°

which gives, ∠A+∠B=180 and, ∠A+∠D=180°

Showing, AB║CD, and AD║BC.

Join ,either, AC or BD.

So, By AAS,we can prove that ,the two triangles are congruent.

So, Quadrilateral ABCD is a Parallelogram.

III.Both pairs of opposite sides are congruent.→Axiom

V.Both pairs of opposite sides are parallel. →→Proved in I

VI.One pair of opposite sides are both parallel and congruent.

In Quadrilateral ,ABCD

AB║CD,AB=CD

Join AC

In Δ ABC and ΔADC

∠BAC=∠DCA→Alternate interior  Angles

AC is common.

AB=CD→[given]

Δ ABC ≅ ΔADC→→[SAS]

VIII.The diagonals bisect each other.

In ΔAOB and ΔCOD

AO=OC

BO=OD

∠AOB=∠COD→[Vertically opposite angles]

→∠AOB≅∠COD[SAS]

which gives, AB=CD.By taking other two triangles, ∠AOD=∠COB, we can prove, AD=BC.

So, when opposite sides are equal in a Quadrilateral it is a parallelogram.

The Condition which are not Sufficient to prove that a quadrilateral is a parallelogram:

II: A pair of adjacent angles are supplementary.

IV: A pair of opposite angles congruent and a pair of opposite sides congruent.

VI: A pair of opposite sides parallel and the other pair of opposite sides congruent.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

he sells x mount because thats eqivilqant to the maz and then divided into quarters

step-by-step explanation: