SOLUTION: PQRS is a parallelogram . PQ = 2x+6, QR = 8 and RS = x+8 PQ and RS are opposite sides. What are the correct answers? Explain your work. a) The Parallelogram PQRS is a rhombus b

Algebra ->  Parallelograms -> SOLUTION: PQRS is a parallelogram . PQ = 2x+6, QR = 8 and RS = x+8 PQ and RS are opposite sides. What are the correct answers? Explain your work. a) The Parallelogram PQRS is a rhombus b      Log On


   

Question 1075526: PQRS is a parallelogram . PQ = 2x+6, QR = 8 and RS = x+8 PQ and RS are opposite sides. What are the correct answers? Explain your work.
a) The Parallelogram PQRS is a rhombus
b) The diagonals are congruent
c) The length of PS is 8
d) The opposite angles are congruent
e)x = 2
f) The perimeter is 18
Answer by MathLover1(20850) About Me  (Show Source):
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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%2B6,
QR+=+8 and
RS+=+x%2B8+
since PQ and RS are opposite sides =>equal length
PQ=+RS....substitute
2x%2B6=x%2B8 ..........solve for x
2x-x=8-6
x=2
so,
PQ+=+2x%2B6=>PQ+=+2%2A2%2B6=>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