Examples, videos, and solutions to help Grade 8 students learn an informal proof of why dilations are degree-preserving transformations.
• 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.
• We know an informal proof for dilations being degree-preserving transformations that uses the definition of
dilation, the Fundamental Theorem of Similarity, and the fact that there can only be one line through a point
that is parallel to a given line.
• We informally verified that dilations of segments map to segments, dilations of lines map to lines, and dilations of rays map to rays.
Use the diagram below to prove the theorem: Dilations preserve the degrees of angles.
Let there be a dilation from center O with scale factor r. Given ∠PQR, show that P' = dilation(P), Q' = dilation(Q) and R' = dilation(R), then |∠PQR| = |∠P'Q'R'|. That is, show that the image of the angle after a dilation has the same measure, in degrees, as the original.
In this example, students verify that dilations map lines to lines.
In this example, students verify that dilations map segments to segments.
In this example, students verify that dilations map rays to rays.
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