coordinate proof

 

 

Point A= -12,6

Point B= 12,3

Point C=-12, 0

Point D= 12, -3

 

Coordinate Proof

Slope of sides AB: slope=6-3-12-12  = ⅛

Slope of side CD: slope = (0+3)/(-12-12)=⅛

CD is parallel to AB

ABCD is a parallelogram

If a quadrilateral has two pairs of parallel sides then it is a parallelogram

Midpoint of Diagonals

CA=-12+12/2, 0+3/2 = (0, 3/2)

BD= -12+12/2, 6-3/2 = (0, 3/2)

Same midpoint of diagonals

If diagonals have the same midpoint then they bisect each other

If a quad has diagonals which bisect each other, then it is a parallelogram

Slope of sides

AB = ⅛

Side AC = undefined

Sides are not opposite reciprocals of each other, therefore not right angles

If a parallelogram has no right angles, then it can’t be a rectangle

Therefore: The quad is a parallelogram