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MOTION IN GEOMETRY: TRANSFORMATIONS 1.6 Geometry

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CONGRUENCE Figures that match exactly (SHAPE & SIZE) are said to be congruent

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TRANSFORMATIONS The movement of a figure in a plane from its original position, the preimage, to a new position, the image. RIGID TRANSFORMATIONS Transformations that do not change the size or shape of a figure.

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Transformations Preimage The figure before you move it. Usually named with letters Example: A, B, AB… Image The figure after it has been moved Usually named with a letter and a prime symbol (apostrophe) Example: A’, B’, A’B’…

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3 Main Types of Transformations 1.TRANSLATIONS 2.ROTATIONS 3.REFLECTIONS

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TRANSLATIONS Every point of a figure moves in a straight line, and all points move the same distance and in the same direction.

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EXAMPLES

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ACTIVITY 1 Translating an image

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ROTATIONS Every point of a figure moves around a given point known as the center of rotation. All points move the same angle measure.

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EXAMPLES

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ACTIVITY 2 Rotating an image

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REFLECTIONS A line plays the role of a mirror, and every point in a geometric figure is “flipped” across the line.

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EXAMPLES

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ACTIVITY 3, PART 1 The Reflection of a Point

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If a point is reflected across a line, then the line is the ______________ ____________ of the segment that connects the point with its image.

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The Reflection of a Triangle ACTIVITY 3, PART 2

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If a triangle is reflected across a line, then the reflected image of the triangle is ____________ to the original triangle

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Glide Reflection

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A combination of a translation and a reflection.

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