• 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.
Dilations map lines to lines, rays to rays, and segments to segments. Dilations map angles to angles of the same degree.
Examples 1–3: Dilations Map Lines to Lines
Example 4 demonstrates that dilations map rays to rays.
Given center 0 and triangle ABC, dilate the triangle from center 0 with a scale factor r = 3.
a. Note that the triangle ABC is made up of segments AB, BC, and CA. Were the dilated images of these segments still segments?
b. Measure the length of the segments AB and A'B'. What do you notice? (Think about the definition of dilation.)
c. Verify the claim you made in part (b) by measuring and comparing the lengths of BC segments B'C' and segments CA and C'A'. What does this mean in terms of the segments formed between dilated points?
d. Measure ∠ ABC and ∠ A'B'C'. What do you notice?
e. Verify the claim you made in part (d) by measuring and comparing angles ∠ BCA and ∠ B'C'A' and angles ∠ CAB and ∠ C'A'B'. What does that mean in terms of dilations with respect to angles and their degrees?
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