Question

each pair of shapes is congruent. identify a transformation or sequence of transformations that could take one shape to the other.

Explanation:

Step1: Analyze line - segment congruence

For line - segments, if two line - segments are congruent, a translation can map one to the other. For example, if we consider line - segment $AB$ and line - segment $CD$, we can translate line - segment $AB$ so that point $A$ coincides with point $C$ and point $B$ coincides with point $D$ if they are of equal length.

Step2: Analyze triangle congruence

For triangles, if $\triangle DEF$ and $\triangle JKL$ are congruent, we can first translate $\triangle DEF$ so that one of its vertices (say $D$) coincides with the corresponding vertex (say $J$) of $\triangle JKL$. Then, we may need to rotate $\triangle DEF$ around the coincided vertex to make the two triangles match exactly.

Step3: Analyze circle congruence

For circles, since all circles are defined by their center and radius, if two circles are congruent (same radius), we can translate the center of one circle to the center of the other circle.

Answer:

For congruent line - segments like $AB$ and $CD$, a translation can map one to the other. For congruent triangles like $\triangle DEF$ and $\triangle JKL$, a translation followed by a rotation can map one to the other. For congruent circles, a translation of the center of one circle to the center of the other circle can map one to the other.