The transformations we’ve learned about so far, translations, rotations, reflections, and sequences of these motions, are all examples of rigid transformations. A rigid transformation is a move that doesn’t change measurements on any figure.

Earlier, we learned that a figure and its image have corresponding points. With a rigid transformation, figures like polygons also have corresponding sides and corresponding angles. These corresponding parts have the same measurements.

For example, triangle $EFD$ was made by reflecting triangle $ABC$ across a horizontal line, then translating. Corresponding sides have the same lengths, and corresponding angles have the same measures.

Measurements in triangle $ABC$	Corresponding measurements in image $EFD$
$AB = 2.24$	$EF = 2.24$
$BC = 2.83$	$FD = 2.83$
$CA = 3.00$	$DE = 3.00$
angle $ABC = 71.6^\circ$	angle $EFD= 71.6^\circ$
angle $BCA = 45.0^\circ$	angle $FDE= 45.0^\circ$
angle $CAB = 63.4^\circ$	angle $DEF= 63.4^\circ$