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 FI: ( -13,7), ( 1,12)
12- 7/1-( - 13)
5/14
Slope of IN: ( 1,12), ( 15, 7)
7- 12/15- 1
- 5/14
Slope of NE: ( 15, 7), ( 1, -5)
-5- 7/1- 15
6/7
Slope of EF: ( 1, -5), ( -13,7)
7-( -5)/- 13- 1
- 6/7
We can tell that all four sides have different slopes. Next we need to check the lengths of the sides of the quadrilateral. To do that we will use the Distance Formula.
Side
Distance Formula
Simplified
Length of FI: ( -13,7), ( 1,12)
sqrt(( 1-( - 13))^2+( 12- 7)^2)
sqrt(221)
Length of IN: ( 1,12), ( 15, 7)
sqrt(( 15- 1)^2+( 7- 12)^2)
sqrt(221)
Length of NE: ( 15, 7), ( 1, -5)
sqrt(( 1- 15)^2+( -5- 7)^2)
sqrt(340)
Length of EF: ( 1, -5), ( -13,7)
sqrt(( - 13- 1)^2+( 7-( -5))^2)
sqrt(340)
Our quadrilateral has two pairs of consecutive sides congruent and no opposite sides congruent. Therefore, the most precise name for this quadrilateral is a kite.
