Use rigid motions for congruence

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HSG.CO.B.6

**HSG.CO.B.6**: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

HSG.CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

What you'll learn

State the formal definition of congruence in terms of rigid motions: two figures are congruent if and only if there exists a sequence of rigid motions (translations, reflections, rotations) that maps one figure exactly onto the other
Predict the effect of a given rigid motion on a given figure, including the positions of all vertices and the orientation of the image
Apply a sequence of rigid motions to transform a figure and verify that the image coincides with a target figure
Determine whether two given figures are congruent by finding a rigid motion (or sequence of rigid motions) that maps one onto the other, or by arguing that no such rigid motion exists
Explain why the rigid-motion definition of congruence is equivalent to the intuitive notion of "same shape and size"

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Rigid motions and congruence

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