Illustrative Math Alignment: Grade 8 Unit 1

Rigid Transformations and Congruence

Lesson 11: What Is the Same?

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Examples Collection: Transformations	Overview The Transformations collection on Media4Math offers a comprehensive set of 56 math examples, providing educators with a rich resource for teaching geometric transformations. This collection covers a wide range of skills and concepts related to transformations, including translations, reflections, rotations, and dilations.	Definition of Transformations
Math Video Collection: Geometry Applications Video Series: Transformations	Overview This collection aggregates all the math videos and resources in this series: Geometry Applications Video Series: Transformations. There are a total of 12 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.	Applications of Transformations and Definition of Transformations
Closed Captioned Video: Geometry Applications: Transformations	Closed Captioned Video: Geometry Applications: Transformations In this program we look at applications of transformations. We do this in the context of three real-world applications. In the first, we look at translations and rotations in the context of roller coaster rides. In the second example we look at translations in three-dimensional space in the context of cargo ships. In the third example, we look at the design of observatories to look at rotations, reflections, and symmetry.	Definition of Transformations and Applications of Transformations
Closed Captioned Video: Geometry Applications: Transformations, 2	Closed Captioned Video: Geometry Applications: Transformations, Segment 2: 3D Translations. 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.	Definition of Transformations and Applications of Transformations
Closed Captioned Video: Geometry Applications: Transformations, 3	Closed Captioned Video: Geometry Applications: Transformations, Segment 1: Translations and Rotations. Roller coasters provide an ideal opportunity to explore translations and rotations. Displacement vectors are also introduced.	Definition of Transformations and Applications of Transformations
Closed Captioned Video: Geometry Applications: Transformations, 3	Closed Captioned Video: Geometry Applications: Transformations, Segment 3: Rotations, Reflections, and Symmetry. 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.	Definition of Transformations and Applications of Transformations
Math Example--Geometric Shapes--Congruent Triangles--Example 1	Math Example--Geometric Shapes--Congruent Triangles--Example 1 Topic Geometry Description This image shows two triangles labeled ABC and DEF. The triangles are oriented differently but have corresponding sides and angles marked as congruent. The table below the triangles lists the congruent sides and angles. In this topic, students explore principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 2	Math Example--Geometric Shapes--Congruent Triangles--Example 2 Topic Geometry Description This image shows two triangles labeled ABC and DEF. The triangles are oriented differently, but the corresponding sides are marked as congruent. The given information lists AB ≅ FE, AC ≅ DF, and BC ≅ DE. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 3	Math Example--Geometric Shapes--Congruent Triangles--Example 3 Topic Geometry Description This image shows two triangles labeled ABC and DEF. The triangles have corresponding angles marked as congruent (∠A ≅ ∠D, ∠B ≅ ∠E, ∠C ≅ ∠F). However, no information is given about the side lengths. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 4	Math Example--Geometric Shapes--Congruent Triangles--Example 4 Topic Geometry Description This image shows two triangles ABD and CBD sharing a common side BD. Given information includes AD ≅ CD and AB ≅ BC. The solution points out that BD is common to both triangles and uses this to conclude that the triangles are congruent by the SSS Postulate. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 5	Math Example--Geometric Shapes--Congruent Triangles--Example 5 Topic Geometry Description The image shows two triangles, each intersecting a circle at two points and one of whose angles is a central angle. The triangles are ABC and DCE. We are given that AB ≅ DE. Furthermore, each triangle has two sides that correspond to radii of the circle and therefore those sides are congruent. As a result of the SSS Postulate, since corresponding sides of the triangle are congruent, then the triangles are congruent.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 6	Math Example--Geometric Shapes--Congruent Triangles--Example 6 Topic Geometry Description The image displays two triangles. The left triangle is labeled ABC. The right triangle is labeled DEF. We are given congruent corresponding sides and angles. Using the SAS Postulate, the two triangles are congruent. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 7	Math Example--Geometric Shapes--Congruent Triangles--Example 7 Topic Geometry Description The image shows two triangles. The left triangle is labeled ABC . The right triangle is labeled DEF. We are given pairs of corresponding angles and corresponding sides. Using the AAS Postulate, we can prove the triangles are congruent. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	Definition of a Triangle
Math Example--Geometric Shapes--Congruent Triangles--Example 8	Math Example--Geometric Shapes--Congruent Triangles--Example 8 Topic Geometry Description The image depicts two triangles. The left triangle is labeled ABC. The right triangle is labeled DEF. We are given pairs of corresponding angles and a pair of corresponding sides. Using the ASA Postulate, the two triangles are congruent. In this topic, students explore the principles of Geometry, particularly focusing on congruence in geometric shapes. Examples like this help build an understanding of how congruence is determined by matching angles and sides.	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
Math Example--Geometric Transformation--Transformations: Example 22	Math Example--Geometric Transformation--Transformations: Example 22 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. The image shows an uppercase letter "Z" on a grid labeled "Before" and a horizontally shifted version of the same letter on another grid labeled "After." Below, there is an illustration showing just a translation, indicating that the letter "Z" is moved horizontally without any rotation or reflection.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 23	Math Example--Geometric Transformation--Transformations: Example 23 Topic Transformations Description This example illustrates a combination of translation and rotation in geometric transformations. The image shows an uppercase letter "Z" on a grid labeled "Before" and an uppercase letter "N" on another grid labeled "After." Below, there are illustrations showing the two steps of the transformation: first a translation (moving the figure) followed by a rotation (turning the figure). A pushpin indicates the axis of rotation.	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 24	Math Example--Geometric Transformation--Transformations: Example 24 Topic Transformations Description This example demonstrates a combination of reflection and translation in geometric transformations. The image shows an uppercase letter "Z" on a grid labeled "Before" and a rotated and translated version of the same letter in another position on another grid labeled "After." Below, there are illustrations showing the two steps of the transformation: first, a reflection (flipping the figure across an axis shown by the red dashed line) and then a translation (moving the figure).	Definition of Transformations
Math Example--Geometric Transformation--Transformations: Example 25	Math Example--Geometric Transformation--Transformations: Example 25 Topic Transformations Description This example demonstrates a single rotation in geometric transformations. The image shows a transformation of the letter "Z" from an upright position to a rotated position resembling "N". The grid background helps visualize the transformation, and a pushpin icon indicates the axis 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 26	Math Example--Geometric Transformation--Transformations: Example 26 Topic Transformations Description This example illustrates a combination of rotation and reflection in geometric transformations. The image shows a transformation of the letter "Z" into an upside-down "N". A pushpin indicates the axis of rotation, and a red dashed line represents 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 27	Math Example--Geometric Transformation--Transformations: Example 27 Topic Transformations Description This example demonstrates a single reflection in geometric transformations. The image shows a reflection of the letter "Z" across a horizontal red dashed line, resulting in a backward "Z". The grid background helps visualize the reflection, illustrating 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 28	Math Example--Geometric Transformation--Transformations: Example 28 Topic Transformations Description This example demonstrates a complex combination of transformations: translation, rotation, and reflection. The image shows a transformation of the letter "Z" into an upside-down "N". This transformation involves three steps: 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 29	Math Example--Geometric Transformation--Transformations: Example 29 Topic Transformations Description This example demonstrates a simple translation in geometric transformations. The image shows a "Before" and "After" transformation of a black square on a grid. The square moves horizontally to the right, and a dotted arrow indicates the direction of movement. This showcases how an object can move position without changing its size or orientation.	Definition of Transformations
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

Illustrative Math Alignment: Grade 8 Unit 1

Rigid Transformations and Congruence

Lesson 11: What Is the Same?

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