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Isometry

A transformation that does not change the shape or size of a figure

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Types of Isometries

Reflection, translation, and rotation

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Other Names for Isometries

Congruence transformation or rigid motions

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Preimage

The original figure

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Image

Resulting figure

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Reflection

A transformation across a line which is the perpendicular bisector of each segment joining each point and its image

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Reflection across the x-axis

A(x,y)→A’(x,-y)

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Reflection across the y-axis

A(x,y)→A’(-x,y)

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Reflection across the line y=x

A(x,y)→A’(y,x)

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Translation

A transformation where all the points of a figure are moved the same direction. The image is congruent to the preimage and when transformed along a vector the image has the same length as the vector and is parallel to the vector.

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Translation along a Vector

A(x,y)→A’(x+a,y+b)

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Rotation

A transformation that turns a figure around a fixed point.

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Center of Rotation

The fixed point around which a rotation is made

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Line of Reflection

A straight line across which a reflection is made

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Rotation by 90 about the Origin

A(x,y)→A’(-y,x)

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Rotation by 180 about the Origin

A(x,y)→A’(-x,-y)

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Composition of Transformation

One transformation followed by another

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Glide Reflection

The composition of a translation and a reflection across a line parallel to the translation vector

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Isometry

A composition of two isometries is a(n) _______.

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Translation

The composition of two reflections across two parallel lines is equivalent to a(n) _______.

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Rotation

The composition of two reflections across two intersecting lines is equivalent to a(n) __________.

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Reflections

Any translation or rotation is equivalent to a composition of two ___________.

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Symmetry

A figure has __________ if there is a transformation of the figure such that the image coincides with the preimage

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Line Symmetry

A figure has ______ if it can be reflected across a line so that the image coincides with the preimage

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Line of Symmetry

Divides the figure into two congruent halves

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Rotational Symmetry

A figure has ___________ if it can be rotated about a point by an angle greater than 0 and less than 360 so that the image coincides with the preimage

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Plane Symmetry

A three-dimensional figure has ________ if a plane can divide the figure into two congruent reflected halves

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