Question

What are two similarties between determining what type of quadrilateral is on coordinate plane and what type of triangle is on coordinatinate plane?

Answer 1

I would say finding the lengths of the sides because in a quadrilateral, that might help determine whether the quadrilateral is a parallelogram or rhombus or some other speciall type of quadrilateral based on lengths of sides. The same holds true for a triangle to determine if the triangle is isosceles or equilateral, distinctions both based on lengths of sides.
Finding the slopes of two adjacent sides or 2 opposite sides is another similarity. In the case of a quadrilateral, the slopes might determine perpendicular or parallel sides which in turn would lead to the quadrilateral being special such as a rectangle or a parallelogram. In the triangle, there are no opposite pairs of sides but the slopes of two adjacent sides might determine if the triangle is a right triangle.