Question

rotate the figure $180^{\circ}$ counterclockwise about the origin. then decide if each statement about rotated figures is true or false.

statement about rotated figures true false
if two sides are parallel in the original figure, then those sides may not be parallel in the final figure. ○ ○
the final side lengths are the same as the original side lengths. ○ ○
the final angle measures are smaller than the original angle measures. ○ ○
the original figure and the final figure may not be congruent. ○ ○

Explanation:

Step1: Identify original vertices

Original triangle vertices: $(1,1)$, $(1,4)$, $(5,1)$

Step2: Apply 180° rotation rule

Rotation rule: $(x,y) \to (-x,-y)$
New vertices: $(-1,-1)$, $(-1,-4)$, $(-5,-1)$

Step3: Analyze rotation properties

Rotations are rigid transformations: preserve side lengths, angles, parallelism, and congruence.

Answer:

1. If two sides are parallel in the original figure, then those sides may not be parallel in the final figure.: False
2. The final side lengths are the same as the original side lengths.: True
3. The final angle measures are smaller than the original angle measures.: False
4. The original figure and the final figure may not be congruent.: False