Students learn the definition of dilation and why “same shape” is not good enough to say two figures are similar.
Students know that dilations magnify and shrink figures.
Students learn how to use a compass and a ruler to perform dilations.
Students learn that dilations map lines to lines, segments to segments, and rays to rays. Students know that dilations are degree preserving.
Students know that dilations map circles to circles and ellipses to ellipses with the same shape.
Students know that to shrink or magnify a dilated figure back to its original size from center 0 with scale factor r you must dilate the figure by a scale factor of 1/r.
Students experimentally verify the properties related to the Fundamental Theorem of Similarity (FTS).
Students verify the converse of the Fundamental Theorem of Similarity experimentally.
Students apply the Fundamental Theorem of Similarity to find the location of dilated points on the plane.
Students describe the effect of dilations on two - dimensional figures using coordinates.
Students know an informal proof of why dilations are degree - preserving transformations.
Students know an informal proof of why dilations map segments to segments, lines to lines , and rays to rays.