We can tell that the consecutive sides are not perpendicular, as their slopes are not opposite reciprocals.
1/2 * 1/2 ≠- 1
Since rectangles and squares have perpendicular sides, our parallelogram can only be a rhombus or none of the given types of parallelograms. To check if it is a rhombus, we can find the lengths of its sides using the Distance Formula.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Simplify
LM
L( 1,2), M( 3,3)
sqrt(( 3- 1)^2+( 3- 2)^2)
sqrt(5)
MN
M( 3,3), N( 5, 2)
sqrt(( 5- 3)^2+( 2- 3)^2)
sqrt(5)
NP
N( 5, 2), P( 3, 1)
sqrt(( 3- 5)^2+( 1- 2)^2)
sqrt(5)
PL
P( 3, 1), L( 1,2)
sqrt(( 1- 3)^2+( 2- 1)^2)
sqrt(5)
Our parallelogram has four congruent sides, that are not perpendicular. Therefore, the most precise name for this parallelogram is rhombus.
