Write a two-column proof for the following conjuncture. you may not need to use all of the rows of the two-column table provided below. you may also add additional rows if needed given parallelogram abcd
(given 7 columns on assignment)

prove: angle a and angle b are supplementary
angle b and angle c are supplementary.

For any parallelogram, each two opposite sides are parallel and equal.

So, for the given ABCD be a parallelogram

AB // CD and CB is a transversal.

Because of the sum of the interior angles on the same side of the transversal is 180°

So, ∠B + ∠C = 180°

∴ Angle B and angle C are supplementary.

And

AD // BC and AB is a transversal.

Because of the sum of the interior angles on the same side of the transversal is 180°

So, ∠A + ∠B = 180°

∴ Angle A and angle B are supplementary.

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.