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: ( 1,2), ( 11,2)
2- 2/11- 1
0
Slope of BC: ( 11,2), ( 7,5)
5- 2/7- 11
- 3/4
Slope of CD: ( 7, 5), ( 4,5)
5- 5/4- 7
0
Slope of DA: ( 4,5), ( 1,2)
2- 5/1- 4
1
We can tell that the slopes of two opposite sides of our quadrilateral are equal. Therefore, the pair of opposite sides are parallel and the quadrilateral is either a trapezoid or an isosceles trapezoid. To check, we can find the lengths of its legs using the Distance Formula.
Side
Distance Formula
Simplified
Length of AD: ( 1,2), ( 4,5)
sqrt(( 4- 1)^2+( 5- 2)^2)
sqrt(18)
Length of BC: ( 11,2), ( 7, 5)
sqrt(( 7- 11)^2+( 5- 2)^2)
sqrt(25)
The legs of the trapezoid are different lengths, so the most precise name for this quadrilateral is a trapezoid.
