In each exercise a glide reflection is described. Graph A B C and its image under the glide, A^'

step 1 As you can see, all properties remain invariant except for

In each exercise a glide reflection is described. Graph A B...

In each exercise a glide reflection is described. Graph $\triangle A B C$ and its image under the glide, $\triangle A^{\prime} B^{\prime} C^{\prime}$ . Also graph $\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime},$ the image of $\triangle A^{\prime} B^{\prime} C^{\prime}$ under the reflection. Which of the properties listed in Exercise 11 are invariant under a glide reflection?

In each exercise a glide reflection is described. Graph $\triangle A B C$ and its image under the glide, $\triangle A^{\prime} B^{\prime} C^{\prime}$ . Also graph $\triangle A^{\prime \prime} B^{\prime \prime} C^{\prime \prime},$ the image of $\triangle A^{\prime} B^{\prime} C^{\prime}$ under the reflection.
Which of the properties listed in Exercise 11 are invariant under a glide reflection?

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Key Concepts

Invariant Properties Under Rigid Motions

Invariant properties refer to the characteristics of a geometric figure that remain unchanged under rigid motions, such as isometries. For glide reflections, properties like the lengths of sides and the measures of angles are preserved, while properties related to orientation may change.

Glide Reflection

A glide reflection is a composite isometry that combines a reflection across a line with a translation along that line. This type of transformation preserves the shape and size of geometric figures, meaning that lengths and angle measures remain unchanged, although the overall orientation is reversed due to the reflection component.

Isometry

Isometries are transformations that preserve distances and angles, ensuring that the original figure and its image are congruent. Examples include translations, rotations, reflections, and glide reflections, all of which maintain the size and shape of geometric figures even if their positions or orientations change.

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