Rhombus proof
rhombus proof
Begin with a given line AC. Given that a circle is the set of all points equidistant from a given point, construct a circle centered on one of the endpoints of the line AC. The radius of the circle, the distance of any given point on the circle from the center point, should be larger than the line created by connecting an endpoint of AC to the point that bisects (cuts in half) the line AC. Once you have created this circle, create another circle with the same radius that is centered at the other endpoint of AC. Notice, these circles intersect at two points. By connecting the endpoints of AC to the intersection points of the circles, you have created a rhombus. We know it is a rhombus because each side of the rhombus happens to be a radius of one of the two identical circles, thus all four sides are the same length.