Illustrative Math Alignment: Grade 8 Unit 1
Rigid Transformations and Congruence
Lesson 4: Making the Moves
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Geometric Transformation--Transformations: Example 4 | Math Example--Geometric Transformation--Transformations: Example 4TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. Two "T" shapes are shown on a grid, labeled "Before" and "After". The shape undergoes a rotation around a point indicated by a pushpin, which serves as the axis of rotation. This illustrates how an object can change its orientation without altering its size or position relative to the rotation point. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 40 | Math Example--Geometric Transformation--Transformations: Example 40TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. A pushpin indicates the axis of rotation, and a red dashed line shows the axis of reflection. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 41 | Math Example--Geometric Transformation--Transformations: Example 41TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. The image shows two hexagons on a grid, labeled "Before" and "After." The hexagon is reflected over a vertical axis, with a red dashed line indicating the reflection axis. This illustrates how an object can be flipped over a line while maintaining its size and shape but changing its orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 42 | Math Example--Geometric Transformation--Transformations: Example 42TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows two hexagons on a grid, labeled "Before" and "After." There are three transformations: first, a translation moves the shape, then a rotation turns it (indicated by a pushpin showing the axis of rotation), and finally, a reflection flips it across a red dashed line representing the axis of reflection. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 43 | Math Example--Geometric Transformation--Transformations: Example 43TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. The image shows two house icons on a grid, labeled "Before" and "After." The house is translated horizontally to the right, with an arrow indicating the movement direction. This showcases how an object can move position without changing its size or orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 44 | Math Example--Geometric Transformation--Transformations: Example 44TopicTransformations DescriptionThis example illustrates a combination of translation and rotation in geometric transformations. The image shows two house icons on a grid, labeled "Before" and "After." Two transformations occur: translation (shown by an arrow) and rotation (shown by a pushpin). This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 45 | Math Example--Geometric Transformation--Transformations: Example 45TopicTransformations DescriptionThis example demonstrates a combination of reflection and translation in geometric transformations. The image shows two figures labeled as "Before" and "After." The left figure illustrates a shape on a grid, while the right figure shows the same shape after a transformation involving reflection and translation, marked with a dashed red line. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 46 | Math Example--Geometric Transformation--Transformations: Example 46TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. The image presents two figures labeled "Before" and "After." The left figure shows a shape on a grid, while the right one displays the same shape after a rotation around a specified point marked with a pushpin. This illustrates how an object can change its orientation without altering its size or shape. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 47 | Math Example--Geometric Transformation--Transformations: Example 47TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. Two figures are presented, labeled "Before" and "After." The left figure shows the original shape on a grid, while the right figure depicts the shape after undergoing a combination of transformations: first, a rotation around a point indicated by a pushpin, followed by a reflection across a dashed red line. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 48 | Math Example--Geometric Transformation--Transformations: Example 48TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. The image shows two figures labeled as "Before" and "After." The left figure includes a shape positioned within a grid, and the right figure illustrates the transformed shape after reflecting across a dashed red line. This showcases how an object can be flipped over a line while maintaining its size and shape but changing its orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 49 | Math Example--Geometric Transformation--Transformations: Example 49TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows two house-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. The transformation involves three steps: first, a translation moves the shape, then a rotation turns it around an axis marked by a pushpin, and finally, a reflection flips it across a dashed red line representing the axis of reflection. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 5 | Math Example--Geometric Transformation--Transformations: Example 5TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The shape first undergoes a rotation, indicated by a pushpin showing the axis of rotation, and then a reflection, shown by a red dashed line representing the axis of reflection. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 50 | Math Example--Geometric Transformation--Transformations: Example 50TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. The transformation consists of a simple translation from left to right, showcasing how an object can move position without changing its size or orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 51 | Math Example--Geometric Transformation--Transformations: Example 51TopicTransformations DescriptionThis example illustrates a combination of translation and rotation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right. There are two transformations: first, a translation moves the shape, then a rotation turns it around an axis marked by a pushpin. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 52 | Math Example--Geometric Transformation--Transformations: Example 52TopicTransformations DescriptionThis example demonstrates a combination of reflection and translation in geometric transformations. The image shows two star-shaped figures on a grid. The "Before" figure is on the left, and the "After" figure is on the right, located lower and to the right. There are two transformations: first, a reflection across an axis shown by a red dashed line, followed by a translation to move the shape to its final position. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 53 | Math Example--Geometric Transformation--Transformations: Example 53TopicTransformations DescriptionThis example demonstrates a single rotation in geometric transformations. The image shows a star on a grid labeled "Before" and "After." The star has been rotated to a new position on the grid, as indicated by a pushpin that marks the axis of rotation. This illustrates how an object can change its orientation without altering its size or shape. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 54 | Math Example--Geometric Transformation--Transformations: Example 54TopicTransformations DescriptionThis example illustrates a combination of rotation and reflection in geometric transformations. The image displays a star on a grid with "Before" and "After" labels. The transformation involves two steps: first, a rotation around an axis marked by a pushpin, and second, a reflection across a vertical axis shown by a red dashed line. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in orientation and position. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 55 | Math Example--Geometric Transformation--Transformations: Example 55TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. In this image, a star is shown before and after undergoing a reflection. The red dashed line represents the axis of reflection, which is horizontal in this case. This showcases how an object can be flipped over a line while maintaining its size and shape but changing its orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 56 | Math Example--Geometric Transformation--Transformations: Example 56TopicTransformations DescriptionThis example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows three transformations applied to the star: first, a translation moves the star to another position, then a rotation turns it around an axis indicated by a pushpin, and finally a reflection flips it across a vertical axis shown by a red dashed line. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 6 | Math Example--Geometric Transformation--Transformations: Example 6TopicTransformations DescriptionThis example demonstrates a single reflection in geometric transformations. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below illustrates a reflection of the shape across a red dashed line, which represents the axis of reflection. This transformation showcases how an object can be flipped over a line while maintaining its size and shape. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 7 | Math Example--Geometric Transformation--Transformations: Example 7TopicTransformations DescriptionThis example illustrates a complex combination of transformations: translation, rotation, and reflection. Two grids labeled "Before" and "After" show a black "T" shape in different orientations. The solution diagram below demonstrates three sequential transformations: first, a translation moves the shape, then a rotation turns it (indicated by a pushpin showing the axis of rotation), and finally, a reflection flips it across a red dashed line representing the axis of reflection. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 8 | Math Example--Geometric Transformation--Transformations: Example 8TopicTransformations DescriptionThis example demonstrates a simple translation in geometric transformations. Two grids labeled "Before" and "After" show an "O" shape slightly shifted between the grids. The solution diagram below illustrates a translation of the shape from one position to another, showcasing how an object can move position without changing its size or orientation. |
Definition of Transformations |
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Math Example--Geometric Transformation--Transformations: Example 9 | Math Example--Geometric Transformation--Transformations: Example 9TopicTransformations DescriptionThis example illustrates a combination of transformations: translation and rotation. Two circular "O" shapes are shown on a grid, one labeled "Before" and the other "After". The solution involves a translation (movement) and a rotation, with a pushpin indicating the axis of rotation. This demonstrates how multiple transformations can be applied sequentially to a shape. |
Definition of Transformations |
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Math Example--Geometric Transformation--Translating Triangles--Example 1 | Math Example--Geometric Transformation--Translating Triangles--Example 1TopicTransformations DescriptionA triangle on a grid is translated 4 units to the left. It shows the original triangle ABC and the translated triangle A'B'C'. Example 1: "Draw the triangle that results from the following translation: 4 units to the left." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 10 | Math Example--Geometric Transformation--Translating Triangles--Example 10TopicTransformations Description
The triangle is translated 4 units to the left and 2 units up. It displays both the initial and the translated triangles. Example 10: "Draw the triangle that results from the following translation: 4 units to the left, 2 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 11 | Math Example--Geometric Transformation--Translating Triangles--Example 11TopicTransformations DescriptionTriangle ABC is translated horizontally to the right by 4 units to form triangle A'B'C'. Example 11: The translation is described as 4 units to the right. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 12 | Math Example--Geometric Transformation--Translating Triangles--Example 12TopicTransformations DescriptionTriangle ABC is translated vertically downward by 6 units to form triangle A'B'C'. Example 12: The translation is described as 6 units down. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 13 | Math Example--Geometric Transformation--Translating Triangles--Example 13TopicTransformations DescriptionTriangle ABC is translated horizontally to the left by 5 units to form triangle A'B'C'. Example 13: The translation is described as 5 units to the left. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 14 | Math Example--Geometric Transformation--Translating Triangles--Example 14TopicTransformations DescriptionTriangle ABC is translated vertically upward by 6 units to form triangle A'B'C'. Example 14: The translation is described as 6 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 15 | Math Example--Geometric Transformation--Translating Triangles--Example 15TopicTransformations Description
Triangle ABC is translated diagonally 5 units to the right and 5 units downward to form triangle A'B'C'. Example 15: The translation is described as 5 units to the right and 5 units down. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 16 | Math Example--Geometric Transformation--Translating Triangles--Example 16TopicTransformations DescriptionTriangle ABC is translated diagonally 4 units to the right and 3 units upward to form triangle A'B'C'. Example 16: The translation is described as 4 units to the right and 3 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 17 | Math Example--Geometric Transformation--Translating Triangles--Example 17TopicTransformations DescriptionTriangle ABC is translated diagonally 4 units downward and 4 units to the right to form triangle A'B'C'. Example 17: The translation is described as 4 units down and 4 units to the right. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 18 | Math Example--Geometric Transformation--Translating Triangles--Example 18TopicTransformations Description
Triangle ABC is translated diagonally 3 units upward and 3 units to the right to form triangle A'B'C'. Example 18: The translation is described as 3 units up and 3 units to the right. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 19 | Math Example--Geometric Transformation--Translating Triangles--Example 19TopicTransformations DescriptionTriangle ABC is translated diagonally 6 units to the left and 4 units downward to form triangle A'B'C'. Example 19: The translation is described as 6 units to the left and 4 units down. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 2 | Math Example--Geometric Transformation--Translating Triangles--Example 2TopicTransformations DescriptionA triangle on a grid is translated 5 units to the right. The diagram shows the original triangle ABC and the new position, A'B'C'.. Example 2: "Draw the triangle that results from the following translation: 5 units to the right." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 20 | Math Example--Geometric Transformation--Translating Triangles--Example 20TopicTransformations DescriptionTriangle ABC is translated diagonally 2 units to the left and 5 units upward to form triangle A'B'C'. Example 20: The translation is described as 2 units to the left and 5 units up. In this topic, students explore transformations, focusing specifically on translating triangles. These examples visually demonstrate how shapes move within a coordinate plane, reinforcing understanding of shifts along axes. Translation examples assist in grasping the basic concept of shifting figures without altering their orientation or shape. |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 21 | Math Example--Geometric Transformation--Translating Triangles--Example 21TopicTransformations |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 22 | Math Example--Geometric Transformation--Translating Triangles--Example 22TopicTransformations |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 3 | Math Example--Geometric Transformation--Translating Triangles--Example 3TopicTransformations DescriptionA triangle on a grid is translated 4 units up. The figure displays both the original and translated triangles ABC and A'B'C'.. Example 3: "Draw the triangle that results from the following translation: 4 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 4 | Math Example--Geometric Transformation--Translating Triangles--Example 4TopicTransformations DescriptionA triangle on a grid is translated 5 units down. It shows the original triangle and its new position after translation, labeled A'B'C'. Example 4: "Draw the triangle that results from the following translation: 5 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 5 | Math Example--Geometric Transformation--Translating Triangles--Example 5TopicTransformations DescriptionA triangle is translated 4 units to the left and 2 units down. Both the original and the new triangles, ABC and A'B'C', are illustrated. Example 5: "Draw the triangle that results from the following translation: 4 units to the left, 2 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 6 | Math Example--Geometric Transformation--Translating Triangles--Example 6TopicTransformations DescriptionThe triangle is translated 5 units to the right and 3 units up. The image includes both original and translated triangles, labeled ABC and A'B'C'. Example 6: "Draw the triangle that results from the following translation: 5 units to the right, 3 units up." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 7 | Math Example--Geometric Transformation--Translating Triangles--Example 7TopicTransformations DescriptionA triangle is translated 4 units up and 5 units left, showing the original ABC and translated A'B'C' triangles. Example 7: "Draw the triangle that results from the following translation: 4 units up, 5 units left." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 8 | Math Example--Geometric Transformation--Translating Triangles--Example 8TopicTransformations Description
The triangle is translated 5 units up and 2 units right. The image shows both the original and translated positions of the triangle. Example 8: "Draw the triangle that results from the following translation: 5 units up, 2 units rogjt." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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Math Example--Geometric Transformation--Translating Triangles--Example 9 | Math Example--Geometric Transformation--Translating Triangles--Example 9TopicTransformations DescriptionA triangle is translated 4 units to the right and 3 units down. The image shows both the original and the new triangle positions. Example 9: "Draw the triangle that results from the following translation: 4 units to the right, 3 units down." Solution: "Identify one point to translate. Then complete the triangle." |
Applications of Transformations and Applications of Triangles |
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MATH EXAMPLES--Teacher's Guide: Transformations | MATH EXAMPLES--Teacher's Guide: Transformations
This set of tutorials provides 56 examples of transformations of geometric figures on a graph. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Transformations and Definition of Transformations |
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MATH EXAMPLES--Transformations | MATH EXAMPLES--Transformations
This set of tutorials provides 56 examples of transformations of geometric figures on a graph. NOTE: The download is a PPT file. |
Applications of Transformations and Definition of Transformations |
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Promethean Flipchart: Geometry Applications: Transformations 1 | Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Transformations, Segment 1: Translations and Rotations]: https://www.media4math.com/library/geometry-applications-transformations-segment-1-translations-and-rotations This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-1-translations-and-rotations |
Applications of Transformations |
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Promethean Flipchart: Geometry Applications: Transformations 2 | Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations. Note: The download for this resources is the Promethean Flipchart. To access the full video [Geometry Applications: Transformations, Segment 2: 3D Translations]: https://www.media4math.com/library/geometry-applications-transformations-segment-2-3d-translations This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-transformations-segment-2-3d-translations |
Applications of Transformations |
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Promethean Flipchart: Geometry Applications: Transformations 3 | The Gemini telescope in Hawaii is an example of architecture that moves. All observatories rotate in order to follow objects in the sky. This also provides an opportunity to explore rotations, reflections, and symmetry. Note: The download for this resources is the Promethean Flipchart. The full video [Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry] can be found here: https://media4math.com/library/geometry-applications-transformations-segment-3-rotations-reflections-and-symmetry |
Applications of Transformations |
