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MOTION IN GEOMETRY: TRANSFORMATIONS 1.6 Geometry.

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Presentation on theme: "MOTION IN GEOMETRY: TRANSFORMATIONS 1.6 Geometry."— Presentation transcript:

1 MOTION IN GEOMETRY: TRANSFORMATIONS 1.6 Geometry

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

3 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.

4 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’…

5 3 Main Types of Transformations 1.TRANSLATIONS 2.ROTATIONS 3.REFLECTIONS

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

7 EXAMPLES

8 ACTIVITY 1 Translating an image

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

10 EXAMPLES

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12 ACTIVITY 2 Rotating an image

13 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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15 EXAMPLES

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17 ACTIVITY 3, PART 1 The Reflection of a Point

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

19 The Reflection of a Triangle ACTIVITY 3, PART 2

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

21 Glide Reflection

22 A combination of a translation and a reflection.

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