Illustrative Math Alignment: Grade 8 Unit 1

Rigid Transformations and Congruence

Lesson 9: Composing Figures

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Geometric Transformation--Transformations: Example 3	Math Example--Geometric Transformation--Transformations: Example 3 Topic Transformations Description This example showcases a combination of reflection and translation in geometric transformations. Two "T" shapes are displayed on a grid, labeled "Before" and "After". The shape is first reflected across a red dashed line (the axis of reflection) and then translated to a new position. This demonstrates how multiple transformations can be applied in sequence to create more complex movements.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 30	Math Example--Geometric Transformation--Transformations: Example 30 Topic Transformations Description This example illustrates a combination of translation and rotation in geometric transformations. The image depicts a "Before" and "After" transformation of a black square on a grid. The square moves down and rotates 90 degrees clockwise. A pushpin marks the axis of rotation, and dotted arrows indicate the movement and rotation. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 31	Math Example--Geometric Transformation--Transformations: Example 31 Topic Transformations Description This example demonstrates a combination of reflection and translation in geometric transformations. The image shows a "Before" and "After" transformation of a black rectangle on a grid. The rectangle first reflects across a horizontal axis, marked by a red dashed line, and then translates horizontally to the right. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 32	Math Example--Geometric Transformation--Transformations: Example 32 Topic Transformations Description This example demonstrates a single rotation in geometric transformations. The image shows a "Before" and "After" transformation of a black rectangle on a grid. The rectangle rotates 90 degrees clockwise around an axis marked by a pushpin. This illustrates how an object can change its orientation without altering its size or shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 33	Math Example--Geometric Transformation--Transformations: Example 33 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. The image shows a transformation of a black L-shaped figure on a grid. The "Before" figure is at the top left, and the "After" figure is at the top right. Below, there is a sequence of two transformations: first, a rotation (indicated by a pushpin showing the axis of rotation), followed by a reflection (shown by a red dashed line representing the axis of reflection).	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 34	Math Example--Geometric Transformation--Transformations: Example 34 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. The image shows a black L-shaped figure on a grid. The "Before" figure is at the top left, and the "After" figure is at the top right. Below, there is a single transformation: a reflection across a vertical axis shown with a red dashed 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
Math Example--Geometric Transformation--Transformations: Example 35	Math Example--Geometric Transformation--Transformations: Example 35 Topic Transformations Description This example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows a black L-shaped figure with a red dot on a grid. The "Before" figure is at the top left, and the "After" figure is at the top right. Below, there are three transformations: first, a translation moves the shape, then a rotation turns it around an axis shown by a pushpin, and finally, a reflection flips it across an axis shown by a red dashed line.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 36	Math Example--Geometric Transformation--Transformations: Example 36 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. The image shows two hexagons on grids. The "Before" figure is at the top left, and the "After" figure is at the top right. Below, there is a single transformation: translation, as indicated by an arrow showing movement from one position to another. This showcases how an object can move position without changing its size or orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 37	Math Example--Geometric Transformation--Transformations: Example 37 Topic Transformations Description This example illustrates a combination of translation and rotation in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. The pushpin indicates the axis of rotation, and the hexagon is translated and rotated. This demonstrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 38	Math Example--Geometric Transformation--Transformations: Example 38 Topic Transformations Description This example demonstrates a combination of reflection and translation in geometric transformations. The image shows a hexagon on a grid, with a "Before" and "After" transformation. A red dashed line shows the axis of reflection, followed by a translation. This illustrates how multiple transformations can be applied sequentially to create more complex changes in position and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 39	Math Example--Geometric Transformation--Transformations: Example 39 Topic Transformations Description This example demonstrates a single rotation 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 only one transformation occurs. This illustrates how an object can change its orientation without altering its size or shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 4	Math Example--Geometric Transformation--Transformations: Example 4 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 40	Math Example--Geometric Transformation--Transformations: Example 40 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 41	Math Example--Geometric Transformation--Transformations: Example 41 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 42	Math Example--Geometric Transformation--Transformations: Example 42 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 43	Math Example--Geometric Transformation--Transformations: Example 43 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 44	Math Example--Geometric Transformation--Transformations: Example 44 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 45	Math Example--Geometric Transformation--Transformations: Example 45 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 46	Math Example--Geometric Transformation--Transformations: Example 46 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 47	Math Example--Geometric Transformation--Transformations: Example 47 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 48	Math Example--Geometric Transformation--Transformations: Example 48 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 49	Math Example--Geometric Transformation--Transformations: Example 49 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 5	Math Example--Geometric Transformation--Transformations: Example 5 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 50	Math Example--Geometric Transformation--Transformations: Example 50 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 51	Math Example--Geometric Transformation--Transformations: Example 51 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 52	Math Example--Geometric Transformation--Transformations: Example 52 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 53	Math Example--Geometric Transformation--Transformations: Example 53 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 54	Math Example--Geometric Transformation--Transformations: Example 54 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 55	Math Example--Geometric Transformation--Transformations: Example 55 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 56	Math Example--Geometric Transformation--Transformations: Example 56 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 6	Math Example--Geometric Transformation--Transformations: Example 6 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 7	Math Example--Geometric Transformation--Transformations: Example 7 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 8	Math Example--Geometric Transformation--Transformations: Example 8 Topic Transformations Description This 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
Math Example--Geometric Transformation--Transformations: Example 9	Math Example--Geometric Transformation--Transformations: Example 9 Topic Transformations Description This 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
Math Example--Geometric Transformation--Translating Triangles--Example 1	Math Example--Geometric Transformation--Translating Triangles--Example 1 Topic Transformations Description A 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
Math Example--Geometric Transformation--Translating Triangles--Example 10	Math Example--Geometric Transformation--Translating Triangles--Example 10 Topic Transformations 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
Math Example--Geometric Transformation--Translating Triangles--Example 11	Math Example--Geometric Transformation--Translating Triangles--Example 11 Topic Transformations Description Triangle 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
Math Example--Geometric Transformation--Translating Triangles--Example 12	Math Example--Geometric Transformation--Translating Triangles--Example 12 Topic Transformations Description Triangle 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
Math Example--Geometric Transformation--Translating Triangles--Example 13	Math Example--Geometric Transformation--Translating Triangles--Example 13 Topic Transformations Description Triangle 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
Math Example--Geometric Transformation--Translating Triangles--Example 14	Math Example--Geometric Transformation--Translating Triangles--Example 14 Topic Transformations Description Triangle 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

Illustrative Math Alignment: Grade 8 Unit 1

Rigid Transformations and Congruence

Lesson 9: Composing Figures

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