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 AR: ( - 2,12), ( 5,8)
8- 12/5-( - 2)
- 4/7
Slope of RG: ( 5,8), ( 2, 5)
5- 8/2- 5
1
Slope of GD: ( 2,5), ( -5,9)
9- 5/- 5- 2
- 4/7
Slope of DA: ( -5,9), ( - 2,12)
12- 9/- 2-( - 5)
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. Let's multiply the slopes of two consecutive sides
1 ( - 4/7 ) = - 4/7
Since the product is - 47≠- 1 the sides are not opposite reciprocals. Therefore, the quadrilateral is either a parallelogram or a rhombus. To check, we can find the lengths of its sides using the Distance Formula.
Side
Distance Formula
Simplified
Length of AR: ( - 2,12), ( 5,8)
sqrt(( 5-( -2 ))^2+( 8- 12)^2)
sqrt(65)
Length of RG: ( 5,8), ( 2, 5)
sqrt(( 2- 5)^2+( 5- 8)^2)
sqrt(18)
Length of GD: ( 2,5), ( -5,9)
sqrt(( - 5- 2)^2+( 9- 5)^2)
sqrt(65)
Length of DA: ( -5,9), ( - 2,12)
sqrt(( - 2-( - 5))^2+( 12- 9)^2)
sqrt(18)
Our quadrilateral has two pairs of congruent sides. Therefore, the most precise name for it is a parallelogram.
