Defining Congruence in Terms of Rigid Motions

Defining Congruence in Terms of Rigid MotionsAdapted from Walch Education

Key ConceptsIf the figure has undergone only rigid motions (translations, reflections, or rotations), then the figures are congruent.If the figure has undergone any non-rigid motions (dilations, stretches, or compressions), then the figures are not congruent. A dilation uses a center point and a scale factor to either enlarge or reduce the figure. A dilation in which the figure becomes smaller can also be called a compression.1.4.2: Defining Congruence in Terms of Rigid Motions2

Key Concepts, continuedA scale factor is a multiple of the lengths of the sides from one figure to the dilated figure. The scale factor remains constant in a dilation.If the scale factor is larger than 1, then the figure is enlarged.If the scale factor is between 0 and 1, then the figure is reduced.1.4.2: Defining Congruence in Terms of Rigid Motions3Key Concepts, continuedTo calculate the scale factor, divide the length of the sides of the image by the lengths of the sides of the preimage.A vertical stretch or compression preserves the horizontal distance of a figure, but changes the vertical distance.A horizontal stretch or compression preserves the vertical distance of a figure, but changes the horizontal distance.1.4.2: Defining Congruence in Terms of Rigid Motions4Key Concepts, continuedTo verify if a figure has undergone a non-rigid motion, compare the lengths of the sides of the figure. If the sides remain congruent, only rigid motions have been performed.If the side lengths of a figure have changed, non-rigid motions have occurred.1.4.2: Defining Congruence in Terms of Rigid Motions51.4.2: Defining Congruence in Terms of Rigid Motions6Non-Rigid Motions: DilationsEnlargement/reductionCompare with . The size of each side changes by a constant scale factor. The angle measures have stayed the same.

1.4.2: Defining Congruence in Terms of Rigid Motions7Non-Rigid Motions: Vertical TransformationsStretch/compressionCompare with . The vertical distance changes by a scale factor. The horizontal distance remains the same. Two of the angles have changedmeasures.

1.4.2: Defining Congruence in Terms of Rigid Motions8Non-Rigid Motions: Horizontal TransformationsStretch/compressionCompare with . The horizontal distance changes by a scale factor. The vertical distance remains the same. Two of the angles have changedmeasures.

Thanks for Watching!Ms. Dambreville