Illustrative Math Alignment: Grade 6 Unit 1

Topic

Equations

Description

This example focuses on solving equations involving parallel lines cut by a transversal, a fundamental concept in geometry. The problem presents two parallel lines intersected by two transversals that also form a triangle. We are given that one angle measures 120° and the corresponding angle can be expressed as (y + 40)°. The goal is to determine the value of y using the properties of angles formed by parallel lines and a transversal. 

When parallel lines are cut by a transversal, several important angle relationships are formed: 

Topic

Equations

Description

This example demonstrates solving equations using the Exterior Angle Theorem in the context of parallel lines cut by a transversal, two crucial concepts in geometry. The problem presents a triangle with two known interior angles of 80° and y, and an unknown exterior angle x°. 

We are also given that 80 - y = 50, which simplifies to y = 30. The goal is to determine the value of x using the properties of triangles and the Exterior Angle Theorem. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Wo we get x = 80 + 30, or x = 110.

Topic

Equations

Description

This example focuses on solving equations involving isosceles triangles centered in a circle. The problem presents two equations: z - y = 20 and z + y = 120, where z and y represent angles in the isosceles triangles. The goal is to solve this system of equations to find the values of z and y, utilizing properties of isosceles triangles and circles. 

Topic

Equations

Description

This example explores solving equations involving triangles that share a vertex at the center of a circle. We are presented with two equations: 

x + y = 75 and z + y = 110, where x, y, and z represent angles in the triangle

The goal is to solve this system of equations to find the values of x, y, and z, utilizing properties of isosceles triangles. Since each of the triangles is isosceles, we know that z + 55 + 55 = 180 and therefore, z = 70°. We substitute this into one of the equations:

70 + y = 110

7 = 40°

Topic

Equations

Description

This example focuses on solving equations involving isosceles triangles with a common vertex and base. We are given two angles, 62° and 99°, and need to find the unknown angle x. This problem demonstrates how to use the properties of isosceles triangles and the sum of angles in a triangle to solve for an unknown angle. 

Key properties to consider: 

Topic

Equations

Description

This example involves solving an equation using the properties of a trapezoid with an embedded parallelogram and applying the exterior angle theorem. We are given two angles, 30° and 110°, and need to find the unknown angle x. This problem demonstrates the application of multiple geometric concepts to solve a complex equation. 

Key properties to consider: 

Topic

Equations

Description

This example focuses on solving equations using the properties of a kite and applying the exterior angle theorem. We are given one angle of 30° and two unknown angles, y and x. The goal is to set up and solve equations to find the values of y and x using the properties of kites and the exterior angle theorem. 

Key properties to consider: 

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This set of tutorials provides 26 examples of how to find the length of a side of a triangle using given angle or side measurements.

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This set of tutorials provides 40 examples of how to find the area and perimeter of triangles.

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To see resources related to this topic click on the Related Resources tab above.

This set of tutorials provides 24 examples that show how to identify different types of triangles and how to solve for x using the properties of triangles.

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To see resources related to this topic click on the Related Resources tab above.

This set of tutorials provides 40 examples of how to find the area and perimeter of triangles. NOTE: The download is a PPT file.

This set of tutorials provides 24 examples that show how to identify different types of triangles and how to solve for x using the properties of triangles. NOTE: The download is a PPT file.

This is the transcript for the video entitled, Desmos Geometry Exploration: Triangle Basics. In this video tutorial the basics of triangles are explored. Students are then shown how to construct triangles using the Desmos geometry tools.

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

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.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Circumscribing a Circle about a Triangle.

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

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Constructing the Circumcenter of a Triangle.

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

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Constructing the Orthocenter of a Triangle.

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

This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts.

This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts.

In this program we explore the properties of triangles. 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.

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.

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 ancient port city of Corinth in Greece allows us to explore the evolution of sailing. The shapes of sails went from rectangular to triangular. The use of right-triangle-shaped sails changed the nature of sailing. Becoming less reliant on oarsmen and being able to sail under nearly any wind conditions, the sailboat made the conquest of the seas possible. We explore the properties of right triangles that make such sails ideal.

In this TI Nspire tutorial, the Geometry window is used to circumscribe a circle about a triangle. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial, the Geometry window is used to construct a triangle and its circumcenter. This video supports the TI-Nspire Clickpad and Touchpad.

In this TI Nspire tutorial the Geometry window is used to construct the orthocenter of a triangle. This video supports the TI-Nspire Clickpad and Touchpad.

This is part of a collection of math worksheets that are crossword puzzles of math vocabulary.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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Worksheet Library

This is part of a collection of math worksheets on the topic of geometric shapes.

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Worksheet Library

This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of using the distance formula to calculate length, area, or perimeter.

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This is part of a collection of math worksheets on the topic of using the distance formula to calculate length, area, or perimeter.

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Worksheet Library