Theorem: In any circles the same ratio of arc length to radius determines a unique central angle that the arcs subtend; and conversely, equal central angles determine the same ratio of arc length to radius. Prove the theorem above using the definition of the radian measure of an angle.

Apolygon is shown on the graph: a polygon is shown on the coordinate plane. vertices are located at 3 comma 5, 1 comma 3, 1 comma 1, 2 comma 0, 4 comma 0, 5 comma 1, and 5 comma 3. what effect will a translation 3 units down and 2 units left have on the polygon? be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image. xd i need