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Defining Congruence in Terms of Rigid Motions

Defining Congruence in Terms of Rigid Motions. Adapted from Walch Education. Key Concepts. If the figure has undergone only rigid motions (translations, reflections, or rotations), then the figures are congruent.

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Defining Congruence in Terms of Rigid Motions

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  1. Defining Congruence in Terms of Rigid Motions Adapted from Walch Education

  2. Key Concepts • If 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 Motions

  3. Key Concepts, continued • A 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 Motions

  4. Key Concepts, continued • To 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 Motions

  5. Key Concepts, continued • To 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 Motions

  6. 1.4.2: Defining Congruence in Terms of Rigid Motions

  7. 1.4.2: Defining Congruence in Terms of Rigid Motions

  8. 1.4.2: Defining Congruence in Terms of Rigid Motions

  9. Thanks for Watching! Ms. Dambreville

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