Question

consider the transformation shown. use the drop-down menus to complete the sentence. the transformation is nonrigid because the drop-down preserved. options: segment lengths are not, segment lengths are, angle measures are not, angle measures are pre-image (triangle with sides 6, 8, 10, right angle) and image (triangle with sides 3, 4, 5, right angle).

Explanation:

Step1: Analyze Rigid vs Nonrigid Transformations

Rigid transformations (like translation, rotation, reflection) preserve segment lengths and angle measures. Nonrigid transformations (like dilation) change segment lengths but preserve angle measures.

Step2: Check Segment Lengths and Angles

Pre - image sides: 6, 8, 10. Image sides: 3, 4, 5. Notice that \(\frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\frac{1}{2}\), so it's a dilation (nonrigid). For angles, the pre - image has a right angle (90°) and the image also has a right angle, and the other angles should be preserved (since dilation is a similarity transformation, angles are congruent). So segment lengths are not preserved, but angle measures are. Since it's nonrigid, we check why: nonrigid transformations don't preserve segment lengths (while angle measures are preserved here). So the correct option for the drop - down is "segment lengths are not".

Answer:

The transformation is nonrigid because the segment lengths are not preserved.