Question

situation #6: parallelogram cats is rotated 90 degrees clockwise about the original to form cats.
shade in the boxes that show which side lengths are parallel.
(the table has rows: sc, st, ac, at and columns: ac, at, sc, st)

Explanation:

Rotations are rigid transformations, meaning they preserve side lengths and parallelism. For a 90-degree clockwise rotation about the origin, each original side maps to its corresponding rotated side, and parallelism is maintained between original sides and their images, as well as between pairs of original parallel sides and their rotated pairs.
In parallelogram CATS, $AC \parallel ST$ and $AT \parallel SC$. After rotation to $C'A'T'S'$, $A'C' \parallel S'T'$ and $A'T' \parallel S'C'$. Additionally, each original side is parallel to its rotated image: $AC \parallel A'C'$, $ST \parallel S'T'$, $AT \parallel A'T'$, $SC \parallel S'C'$.

Answer:

Shade the following pairs (the intersection boxes of each pair):

• $AC$ and $A'C'$
• $AC$ and $ST$
• $ST$ and $S'T'$
• $AT$ and $A'T'$
• $AT$ and $SC$
• $SC$ and $S'C'$
• $A'C'$ and $S'T'$
• $A'T'$ and $S'C'$

In table form (shaded boxes marked with X):

	SC	ST	A'C'	A'T'
AT	X			X
S'C'	X			X
S'T'		X	X