Quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent
Now, let's find the slopes of the sides using the Slope Formula.
Side
Slope Formula
Simplified
Slope of AB: ( 2,4), ( 4,6)
6- 4/4- 2
1
Slope of BC: ( 4,6), ( 6,4)
4- 6/6- 4
- 1
Slope of CD: ( 6,4), ( 4, 2)
2- 4/4- 6
1
Slope of DA: ( 4, 2), ( 2,4)
4- 2/2- 4
- 1
We can tell that the slopes of the opposite sides of our quadrilateral are equal. Therefore, both pairs of opposite sides are parallel and the quadrilateral is a parallelogram. We can also tell that the consecutive side are perpendicular, as their slopes are opposite reciprocals.
1 ( - 1) = -1
Therefore, our quadrilateral is either a rectangle or a square. To check, we can find the lengths of its sides using the Distance Formula.
Side
Distance Formula
Simplified
Length of AB: ( 2,4), ( 4,6)
sqrt(( 4- 2)^2+( 6- 4)^2)
2sqrt(2)
Length of BC: ( 4,6), ( 6, 4)
sqrt(( 6- 4)^2+( 4- 6)^2)
2sqrt(2)
Length of CD: ( 6,4), ( 4,2)
sqrt(( 4- 6)^2+( 2- 4)^2)
2sqrt(2)
Length of DA: ( 4, 2), ( 2,4)
sqrt(( 2- 4)^2+( 4- 2)^2)
2sqrt(2)
Our parallelogram has four congruent sides. Therefore, the most precise name for this quadrilateral is a square.
