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: ( 3,-2), ( 5,4)
4-( -2)/5- 3
3
Slope of BC: ( 5,4), ( 3,6)
6- 4/3- 5
- 1
Slope of CD: ( 3,6), ( 1,4)
4- 6/1- 3
1
Slope of DA: ( 1,4), ( 3,-2)
-2- 4/3- 1
- 3
We can tell that since the slopes of opposite sides are not equal, the pairs of opposite sides cannot be parallel.
Therefore, we suspect that the quadrilateral is a kite. To check, we can find the lengths of its sides using the Distance Formula.
Side
Distance Formula
Simplified
Length of AB: ( 3,-2), ( 5,4)
sqrt(( 5- 3)^2+( 4-( -2))^2)
sqrt(40)
Length of BC: ( 5,4), ( 3,6)
sqrt(( 3- 5)^2+( 6- 4)^2)
sqrt(8)
Length of CD: ( 3,6), ( 1,4)
sqrt(( 1- 3)^2+( 4- 6)^2)
sqrt(8)
Length of DA: ( 1, 4), ( 3,-2)
sqrt(( 3- 1)^2+( -2- 4)^2)
sqrt(40)
Since two pairs of consecutive sides are of the same length, they are congruent. What is more, no opposite sides of the quadrilateral are of the same length. Therefore, the most precise name for this quadrilateral is a kite.
