Answer:
ABCD is a rhombus
Step-by-step explanation:
Sides AB and DC are opposite and equal in parallelogram ABCD. This means ...
AB = CD
2x +1 = 3x -11
12 = x . . . . . . . . add 11-2x to both sides
Sides AB and CD have length ...
2x +1 = 2(12) +1 = 24 +1 = 25
Then the length of side AD is ...
AD = x +13 = 12 +13 = 25
Adjacent sides AB and AD of the parallelogram have the same length, The figure is a rhombus.
Answer:
-7, -6, -3, 2, 9, 18, 29, 42, 57
Rule: + 1, + 3, + 5, + 7, + 9, + 11, + 13, + 15, + 17......................
D is halfway between A and B
so the coordinates of D are (2,2)
E is halfway between A and C so the coordinates of E are (-1,1)
now you need to find the gradient/slope of DE and BC using the formula:

<h3>
<u>G</u><u>r</u><u>a</u><u>d</u><u>i</u><u>e</u><u>n</u><u>t</u><u> </u><u>o</u><u>f</u><u> </u><u>D</u><u>E</u><u>:</u><u> </u></h3>
SUB IN COORDINATES OF D AND E

therefore the gradient of DE is 1/3.
<h3>
<u>G</u><u>r</u><u>a</u><u>d</u><u>i</u><u>e</u><u>n</u><u>t</u><u> </u><u>o</u><u>f</u><u> </u><u>B</u><u>C</u><u>:</u></h3>
<em>S</em><em>U</em><em>B</em><em> </em><em>I</em><em>N</em><em> </em><em>C</em><em>O</em><em>O</em><em>R</em><em>D</em><em>I</em><em>N</em><em>A</em><em>T</em><em>E</em><em>S</em><em> </em><em>O</em><em>F</em><em> </em><em>B</em><em> </em><em>A</em><em>N</em><em>D</em><em> </em><em>C</em>
<em>
</em>
therefore the gradient of BC is -2/-6 which simplifies to 1/3.
<h3>
therefore, BC and DE are parallel as they both have a gradient/slope of 1/3 and parallel lines have the same gradient</h3>