Illustrative Math Alignment: Grade 8 Unit 1

Overview

Overview

The Media4Math collection on Analyzing Congruent Shapes provides a comprehensive set of math examples designed to deepen students' understanding of congruence. These examples cover a range of skills, starting with basic shape identification and progressing to more complex applications of congruence in transformations and geometric reasoning. By presenting examples that increase in complexity, students are guided step-by-step to master the concept of congruence in a structured way.

The Eiffel Tower includes quite a number of exposed triangular trusses. The properties of triangles are used to explore and explain the frequent use of triangular trusses in many building. In particular, isosceles and equilateral triangular trusses are explored. In addition triangle postulates and similarity are explored and analyzed.

Topic

Geometry Basics

Definition

Congruence refers to figures or shapes that have the same size and shape.

Description

Congruence is a fundamental concept in geometry, indicating that two figures are identical in form and dimensions. This concept is essential for understanding geometric transformations and proving the properties of shapes. For instance, two triangles are congruent if their corresponding sides and angles are equal. Congruence is used in various real-world applications, such as engineering and architecture, to ensure precision and accuracy in design and construction.

Topic

Geometry Basics

Definition

Similarity refers to figures that have the same shape but not necessarily the same size.

Description

Similarity is a key concept in geometry, used to compare shapes and solve problems involving proportions. For example, two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. Understanding similarity helps in solving problems related to scaling, resizing, and geometric transformations. This concept is widely used in fields such as art, design, and architecture to create proportional and aesthetically pleasing structures.

This is part of a collection of definitions of geometric theorems and postulates.

This is part of a collection of definitions of geometric theorems and postulates.

This is part of a collection of definitions of geometric theorems and postulates.

This is part of a collection of definitions of geometric theorems and postulates.

This is part of a collection of definitions of geometric theorems and postulates.

This is part of a collection of definitions of geometric theorems and postulates.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

This is from a collection of triangular shapes. They come labeled and unlabeled.

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.

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.

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.

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.

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.

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.

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.

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.

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.

This is the transcript for the video of same title. Video contents: In this program we explore the properties of triangle. We do this in the context of two real-world applications. In the first, we explore the triangular trusses in the Eiffel Tower and in the process learn about key properties of triangles. In the second application, we look at right-triangle-shaped sails on sail boat and why these are the ideal shape for efficient sailing.

This is the transcript for the video of same title. Video contents: The Bank of China building in Hong Kong is a dramatic example of triangular support. The notion of triangular trusses is introduced, along with the key concepts developed in the rest of the program.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: The Eiffel Tower includes quite a number of exposed triangular trusses. The properties of triangles are used to explore and explain the frequent use of triangular trusses in many building. In particular, isosceles and equilateral triangular trusses are explored. In addition triangle postulates and similarity are explored and analyzed.

The Eiffel Tower includes quite a number of exposed triangular trusses. The properties of triangles are used to explore and explain the frequent use of triangular trusses in many building. In particular, isosceles and equilateral triangular trusses are explored. In addition triangle postulates and similarity are explored and analyzed.