8/30/2023 0 Comments Rigid motionUsing your whiteboards: Does this picture show a translation, rotation, or reflection? How do you know? Rotationġ6 Does this picture show a translation, rotation, or reflection?ġ7 The birds were rotated clockwise and the fish counterclockwise. An object and its rotation are the same shape and size, but the figures may be turned in different directions.ġ5 Does this picture show a translation, rotation, or reflection? Clockwise Counterclockwiseġ4 A rotation is a transformation that turns a figure about a fixed point called the center of rotation. This year, we will always rotate about the origin. What is the line of reflection? How did the points change from the original to the reflection?ġ2 The concept of rotations can often be seen in wallpaper designs, fabrics, and art work.ġ3 This rotation is 90 degrees counterclockwise. Name the points of the reflected triangle. Name the points of the original triangle. If you folded the two shapes together line of reflection the two shapes would overlap exactly!ġ1 What happens to points in a Reflection? A reflection can be thought of as a "flipping" of an object over the line of reflection. The distance from a point to the line of reflection is the same as the distance from the point's image to the line of reflection. In a mirror, for example, right and left are switched.ġ0 The line (where a mirror may be placed) is called the line of reflection. An object and its reflection have the same shape and size, but the figures face in opposite directions. We always go left or right first, then up or down.Ĩ A reflection can be seen in water, in a mirror, in glass, or in a shiny surface. The example shows how each vertex moves the same distance in the same direction.ħ In this example, the "slide" moves the figure 7 units to the left and 3 units down. Each coordinate point follows the same rule. The movement of each coordinate point is actually a function. Translations are SLIDESĦ Let's examine some translations related to coordinate geometry. This is referred to as the same orientation. The original object and its translation have the same shape and size, and they face in the same direction. It is common practice to name shapes using capital letters: The original figure is called the pre-image It is common practice to name transformed shapes using the same letters with a “prime” symbol: The transformed figure is called the image.Ī translation "slides" an object a fixed distance in a given direction. The transformations you will learn about include: Translation Rotation Reflection In geometry, there are specific ways to describe how a figure is changed. These transformations lead to the criterion for triangle similarity that two pairs of corresponding angles are congruent.Presentation on theme: "1.3 RIGID MOTIONS."- Presentation transcript:Įssential Question: What properties of a figure are preserved under a translation, reflection, or rotation? September 9, 2014 Similarity transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence, thereby formalizing the similarity ideas of “same shape” and “scale factor” developed in the middle grades. Once these triangle congruence criteria (ASA, SAS, and SSS) are established using rigid motions, they can be used to prove theorems about triangles, quadrilaterals, and other geometric figures. During the middle grades, through experiences drawing triangles from given conditions, students notice ways to specify enough measures in a triangle to ensure that all triangles drawn with those measures are congruent. For triangles, congruence means the equality of all corresponding pairs of sides and all corresponding pairs of angles. In the approach taken here, two geometric figures are defined to be congruent if there is a sequence of rigid motions that carries one onto the other.
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