Illustrative Math Alignment: Grade 8 Unit 1

Rigid Transformations and Congruence

Lesson 1: Moving in the Plane

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 1	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 1 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF also has sides 5, 4, and 6. The SSS Postulate ensures that these triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 1	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 1 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF also has sides 5, 4, and 6. The SSS Postulate ensures that these triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 2	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 2 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF has sides 5, 7, and 6. Because corresponding sides are not all congruent, then the triangles are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 2	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 2 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF has sides 5, 7, and 6. Because corresponding sides are not all congruent, then the triangles are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 2	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 2 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5, 4, and 6, while triangle DEF has sides 5, 7, and 6. Because corresponding sides are not all congruent, then the triangles are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 3	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 3 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6, and triangle DEF has sides 5 and 6, but no information on the third side. As a result, there isn't enough information to know if they are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 3	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 3 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6, and triangle DEF has sides 5 and 6, but no information on the third side. As a result, there isn't enough information to know if they are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 3	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 3 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6, and triangle DEF has sides 5 and 6, but no information on the third side. As a result, there isn't enough information to know if they are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 4	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 4 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Both triangles have two sides (5 and 6) and an included angle of 60°. As a results of the SAS Postulate, the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 4	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 4 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Both triangles have two sides (5 and 6) and an included angle of 60°. As a results of the SAS Postulate, the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 4	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 4 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Both triangles have two sides (5 and 6) and an included angle of 60°. As a results of the SAS Postulate, the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 5	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 5 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6 with an included angle of 60°, and triangle DEF has sides 5 and 6 with an included angle of 62°. Because corresponding angles are not congruent, then the triangles are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 5	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 5 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6 with an included angle of 60°, and triangle DEF has sides 5 and 6 with an included angle of 62°. Because corresponding angles are not congruent, then the triangles are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 5	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 5 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Triangle ABC has sides 5 and 6 with an included angle of 60°, and triangle DEF has sides 5 and 6 with an included angle of 62°. Because corresponding angles are not congruent, then the triangles are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 6	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 6 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Both triangles have angles of 63°, 60°, and 57°, but no information on side lengths. As a result, we can't conclude if the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 6	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 6 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Both triangles have angles of 63°, 60°, and 57°, but no information on side lengths. As a result, we can't conclude if the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 6	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 6 Topic Geometric Shapes Description Determine if two triangles, ABC and DEF, are congruent. Both triangles have angles of 63°, 60°, and 57°, but no information on side lengths. As a result, we can't conclude if the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 7	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 7 Topic Geometric Shapes Description Determine if two triangles on a grid are congruent. Both triangles appear identical in shape and orientation, positioned differently on the grid. Using the grid, you can see that corresponding sides are congruent. Therefore the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 7	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 7 Topic Geometric Shapes Description Determine if two triangles on a grid are congruent. Both triangles appear identical in shape and orientation, positioned differently on the grid. Using the grid, you can see that corresponding sides are congruent. Therefore the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 7	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 7 Topic Geometric Shapes Description Determine if two triangles on a grid are congruent. Both triangles appear identical in shape and orientation, positioned differently on the grid. Using the grid, you can see that corresponding sides are congruent. Therefore the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 8	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 8 Topic Geometric Shapes Description Determine if two shapes on a grid are congruent. The shapes appear as two congruent triangles within a diamond shape, with each triangle reflected across the center axis. Using the grid, you can see that corresonding sides are congruent. Therefore, the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 8	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 8 Topic Geometric Shapes Description Determine if two shapes on a grid are congruent. The shapes appear as two congruent triangles within a diamond shape, with each triangle reflected across the center axis. Using the grid, you can see that corresonding sides are congruent. Therefore, the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 8	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 8 Topic Geometric Shapes Description Determine if two shapes on a grid are congruent. The shapes appear as two congruent triangles within a diamond shape, with each triangle reflected across the center axis. Using the grid, you can see that corresonding sides are congruent. Therefore, the triangles are congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 9	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 9 Topic Geometric Shapes Description Determine if two triangles on a grid are congruent. The triangles have differing shapes and orientations on the grid, suggesting different side lengths or angles. Therefore, they are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 9	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 9 Topic Geometric Shapes Description Determine if two triangles on a grid are congruent. The triangles have differing shapes and orientations on the grid, suggesting different side lengths or angles. Therefore, they are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 9	Math Example--Geometric Shapes--Analyzing Congruent Shapes--Example 9 Topic Geometric Shapes Description Determine if two triangles on a grid are congruent. The triangles have differing shapes and orientations on the grid, suggesting different side lengths or angles. Therefore, they are not congruent. Congruence of shapes is fundamental in geometry as it allows us to establish relationships between figures and understand properties of transformations. This example collection illustrates congruence by analyzing side lengths and angles to determine equivalence.	Definition of a Triangle
Math Example--Geometric Transformation--Transformations: Example 1	Math Example--Geometric Transformation--Transformations: Example 1 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. Two "T" shapes are shown on a grid, labeled "Before" and "After". The "Before" shape on the left is translated to become the "After" shape on the right, illustrating how an object can move position without changing its size or orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 10	Math Example--Geometric Transformation--Transformations: Example 10 Topic Transformations Description This example showcases a combination of reflection and translation in geometric transformations. Two circular "O" shapes are displayed on a grid, one labeled "Before" and the other "After". A red dashed line indicates the axis of reflection. The transformation involves first reflecting the shape across this axis and then translating it 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 11	Math Example--Geometric Transformation--Transformations: Example 11 Topic Transformations Description This example demonstrates a single rotation in geometric transformations. Two circular "O" shapes are shown on a grid, one labeled "Before" and the other "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 12	Math Example--Geometric Transformation--Transformations: Example 12 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. Two circular "O" shapes are displayed on a grid, one labeled "Before" and the other "After". The transformation involves two steps: first, a rotation around a point indicated by a pushpin, which serves as the axis of rotation, followed by a reflection across 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 13	Math Example--Geometric Transformation--Transformations: Example 13 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. Two grids are shown with the letter "O" before and after a transformation. The "Before" grid has the "O" on the left side, while the "After" grid has it on the right side. A red dashed line indicates the axis of reflection in the middle of the two "O"s. Below, there is a diagram showing the reflection transformation along this axis, illustrating how the shape is flipped across the line while maintaining its size and shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 14	Math Example--Geometric Transformation--Transformations: Example 14 Topic Transformations Description This example illustrates a complex combination of transformations: translation, rotation, and reflection. Two grids are shown with an "O" shape before and after transformations. The "Before" grid has an "O" with a red dot at its center, while the "After" grid shows the same "O" but rotated and reflected. Below, a step-by-step diagram illustrates three sequential transformations: first, a translation moves the shape, then a rotation turns it around a pushpin (indicating the axis of rotation), and finally, a reflection flips it across a red dashed line.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 15	Math Example--Geometric Transformation--Transformations: Example 15 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. Two grids are displayed with the letter "F" before and after a transformation. The "Before" grid shows an "F" on the left side, and the "After" grid shows it on the right side. Below, there is an arrow indicating that only a translation occurred between the two positions of the letter, showcasing how an object can move position without changing its size or orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 16	Math Example--Geometric Transformation--Transformations: Example 16 Topic Transformations Description This example demonstrates a combination of translation and rotation in geometric transformations. Two grids are shown with the letter "F" before and after transformations. The "Before" grid has an upright "F", while the "After" grid shows it rotated 90 degrees clockwise. Below, there is a diagram illustrating two steps: first, a translation moves the shape, then a rotation turns it around a pushpin axis.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 17	Math Example--Geometric Transformation--Transformations: Example 17 Topic Transformations Description This example illustrates a combination of reflection and translation in geometric transformations. The image shows a large letter "F" on a grid transforming into a letter "L". The transformation involves two steps: first, a reflection across an axis represented by a red dashed line, and then a translation to a new position.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 18	Math Example--Geometric Transformation--Transformations: Example 18 Topic Transformations Description This example demonstrates a single rotation in geometric transformations. The image shows the letter "F" on a grid being rotated to form the same letter in a different orientation. A pushpin indicates the axis of rotation, and an arrow shows the direction of rotation, illustrating how an object can change its orientation without altering its size or shape.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 19	Math Example--Geometric Transformation--Transformations: Example 19 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. The image shows the letter "F" being transformed into an upside-down version of itself. This transformation involves two steps: first, a rotation around an axis indicated by a pushpin, followed by a reflection across a line represented by a red dashed line.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 2	Math Example--Geometric Transformation--Transformations: Example 2 Topic Transformations Description This example illustrates a combination of transformations: translation and rotation. Two "T" shapes are shown on a grid, labeled "Before" and "After". The shape undergoes 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--Transformations: Example 20	Math Example--Geometric Transformation--Transformations: Example 20 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. The image shows the letter "F" being reflected to form the letter "L". A red dashed line indicates the axis of reflection, illustrating how the letter changes its orientation through this single transformation. This showcases how an object can be flipped over a line while changing its shape and orientation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 21	Math Example--Geometric Transformation--Transformations: Example 21 Topic Transformations Description This example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows an uppercase letter "F" on a grid labeled "Before" and a transformed version of the letter "F" upside down on another grid labeled "After." Below, there are illustrations showing the three steps of the transformation process.	Definition of Transformations

Illustrative Math Alignment: Grade 8 Unit 1

Rigid Transformations and Congruence

Lesson 1: Moving in the Plane

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