Question 1075526

 {{{PQRS}}} is a {{{parallelogram}}} if two pairs of parallel sides, and the opposite or facing sides of a parallelogram are of equal length

a square, rhombus (all sides have equal length) and rectangle are also parallelograms

given:
{{{PQ = 2x+6}}}, 
{{{QR = 8}}} and 
{{{RS = x+8 }}}

since {{{PQ}}} and {{{RS}}} are opposite sides =>{{{equal}}} length

{{{PQ= RS}}}....substitute

{{{2x+6=x+8}}} ..........solve for {{{x}}}

{{{2x-x=8-6}}}

{{{x=2}}}

so, 
{{{PQ = 2x+6}}}=>{{{PQ = 2*2+6}}}=>{{{PQ = 10}}}
{{{RS= 10}}} too 

since {{{QR = 8}}} => forth side is {{{PS=8}}}

so, you have a rectangle and the correct answers are:

b) The diagonals are congruent 
c) The length of {{{PS}}} is {{{8}}}
d) The opposite angles are congruent
e){{{x = 2}}}