You need the midpoint formula,

x(sub 1) + x(sub2) all divided by 2.

and y(sub1) + y(sub2) all divided by 2.

Sub 1 means the first x and sub 2 means the second x.

Then you need the distance formula,

d = square root of[x(sub2) -x(sub1)]^2 +[y (sub 2) -y( sub 1)]^2.

^2 means squared

Then you need the slope formula.

(y sub 2 – y sub 1) divided by( x sub 2 – x sub 1).

1) Draw a triangle on graph paper. Use the mid-point formula to determine the midpoints of the 3 sides. Use the distance formulas to show that the lines connecting the midpoints are half as long as the third sides. Use the slope formula to show they have the same slope and are therefore parallel.

2) Again, draw a quadrilateral on graph paper. Use the midpoint formulas to determine the midpoints of the 4 sides. Connect the midpoints. Use the distance formulas to show that the opposites sides are equal. Use the slope formulas to prove the opposite sides are parallel, thus proving you have a parallelogram.