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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The triangles have different orientation and location. In $△XYZ,$ the vertex $Z$ is to the right of $X$ and $Y.$ In $△X_{′}Y_{′}Z_{′},$ the corresponding vertex $Z_{′},$ is to the left of $X_{′}$ and $Y_{′}.$ To line up their orientations, we can rotate $△XYZ$ $180_{∘}$ about the origin.

Now, by translating the rotated triangle down by $1$ unit and left by 5 units, we can map it onto $△X_{′}Y_{′}Z_{′}.$

Therefore, the congruence transformation that maps $△XYZ$ onto $△X_{′}Y_{′}Z_{′}$ can be written as follows. $Rotation:Translation: 180_{∘}rotation about the origin(x,y)→(x−5,y−1). $