Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 8

Pythagorean Theorem and Irrational Numbers

Lesson 9: The Converse

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Right Triangles-- Example 9 Math Example--Right Triangles-- Example 9 Math Example--Right Triangles-- Example 9

Topic

Right Triangles

 Right Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 1 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 1 Solving Equations Using Triangle Properties: Example 1

Topic

Equations

Description

This example focuses on solving equations using the properties of similar isosceles triangles. Isosceles triangles are characterized by having two equal sides and two equal base angles. In this case, we have two similar isosceles triangles, which means they share the same shape but may differ in size. The equation to be solved involves finding the unknown angle x, given that one of the angles is 20°. The property of vertical angles tells us that the angle vertical to the 20° angle is also 20°

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 10 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 10 Solving Equations Using Triangle Properties: Example 10

Topic

Equations

Description

This example, similar to Example 9, involves solving equations using the properties of a kite and applying the exterior angle theorem. We are again given one angle of 40° 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: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 2 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 2 Solving Equations Using Triangle Properties: Example 2

Topic

Equations

Description

This example explores solving equations using the properties of similar isosceles triangles, building upon the concepts introduced in Example 1. In this case, we have two similar isosceles triangles with one known angle of 70° and an unknown angle x. The goal is to determine the value of x using triangle properties and algebraic techniques. 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 3 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 3 Solving Equations Using Triangle Properties: Example 3

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: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 4 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 4 Solving Equations Using Triangle Properties: Example 4

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.

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 5 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 5 Solving Equations Using Triangle Properties: Example 5

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. 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 6 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 6 Solving Equations Using Triangle Properties: Example 6

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°

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 7 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 7 Solving Equations Using Triangle Properties: Example 7

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: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 8 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 8 Solving Equations Using Triangle Properties: Example 8

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: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 9 Math Example--Solving Equations--Solving Equations Using Triangle Properties: Example 9 Solving Equations Using Triangle Properties: Example 9

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: 

 Applications of Equations and Inequalities and Applications of Triangles
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 1 Solving Equations with Angle Measures--Example 1

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 10 Solving Equations with Angle Measures--Example 10

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 11 Solving Equations with Angle Measures--Example 11

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 12 Solving Equations with Angle Measures--Example 12

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 13 Solving Equations with Angle Measures--Example 13

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 14 Solving Equations with Angle Measures--Example 14

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 15 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 15 Solving Equations with Angle Measures--Example 15

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 2 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 2 Solving Equations with Angle Measures--Example 2

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 3 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 3 Solving Equations with Angle Measures--Example 3

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 4 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 4 Solving Equations with Angle Measures--Example 4

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 5 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 5 Solving Equations with Angle Measures--Example 5

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 6 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 6 Solving Equations with Angle Measures--Example 6

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 7 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 7 Solving Equations with Angle Measures--Example 7

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 8 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 8 Solving Equations with Angle Measures--Example 8

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
Math Example--Solving Equations--Solving Equations with Angle Measures--Example 9 Math Example--Solving Equations--Solving Equations with Angle Measures--Example 9 Solving Equations with Angle Measures--Example 9

Topic

Equations

 Solving Multistep Equations and Applications of Angles and Planes
MATH EXAMPLES--Teacher's Guide: Right Triangles MATH EXAMPLES--Teacher's Guide: Right Triangles MATH EXAMPLES--Teacher's Guide: Right Triangles

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.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

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 Right Triangles
MATH EXAMPLES--Teacher's Guide: Triangle Area and Perimeter MATH EXAMPLES--Teacher's Guide: Triangle Area and Perimeter MATH EXAMPLES--Teacher's Guide: Triangle Area and Perimeter

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

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

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

 Area and Perimeter of Triangles
MATH EXAMPLES--Teacher's Guide: Triangle Classification MATH EXAMPLES--Teacher's Guide: Triangle Classification MATH EXAMPLES--Teacher's Guide: Triangle Classification

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.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

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

 Definition of a Triangle
MATH EXAMPLES--Triangle Area and Perimeter MATH EXAMPLES--Triangle Area and Perimeter MATH EXAMPLES--Triangle Area and Perimeter

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

 Area and Perimeter of Triangles
MATH EXAMPLES--Triangle Classification MATH EXAMPLES--Triangle Classification MATH EXAMPLES--Triangle Classification

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.

 Definition of a Triangle
Paper-and-Pencil Quiz: Distance Formula (Easy) Paper-and-Pencil Quiz: Distance Formula (Easy) Paper-and-Pencil Quiz: Distance Formula (Easy)

This is part of a collection of math quizzes on the topic of the distance formula.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

Related Resources

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Quiz Library

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ary">click on this link.

 Distance Formula and The Distance Formula
Paper-and-Pencil Quiz: Distance Formula (Hard) Paper-and-Pencil Quiz: Distance Formula (Hard) Paper-and-Pencil Quiz: Distance Formula (Hard)

This is part of a collection of math quizzes on the topic of the distance formula.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Quiz Library

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

ary">click on this link.

 Distance Formula and The Distance Formula
Paper-and-Pencil Quiz: Distance Formula (Medium) Paper-and-Pencil Quiz: Distance Formula (Medium) Paper-and-Pencil Quiz: Distance Formula (Medium)

This is part of a collection of math quizzes on the topic of the distance formula.

To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Quiz Library

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

ary">click on this link.

 Distance Formula and The Distance Formula
Video Transcript: Desmos Geometry Exploration: Triangle Basics Video Transcript: Desmos Geometry Exploration: Triangle Basics Video Transcript: Desmos Geometry Exploration: Triangle Basics

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.

This is part of a collection of video transcript for the video tutorial series on using the Desmos Geometry Tools. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

 Definition of a Triangle and Geometric Constructions with Triangles
Video Transcript: Geometry Applications: Triangles Video Transcript: Geometry Applications: Triangles Video Transcript: Geometry Applications: Triangles

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.

 Applications of Triangles
Video Transcript: Geometry Applications: Triangles, Segment 1: Introduction Video Transcript: Geometry Applications: Triangles, Segment 1: Introduction Video Transcript: Geometry Applications: Triangles, Segment 1: Introduction

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.

This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

 Applications of Triangles
Video Transcript: Geometry Applications: Triangles, Segment 2: Triangles Video Transcript: Geometry Applications: Triangles, Segment 2: Triangles Video Transcript: Geometry Applications: Triangles, Segment 2: Triangles

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.

 Applications of Triangles
Video Transcript: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle Video Transcript: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle Video Transcript: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle

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This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

 Geometric Constructions with Triangles
Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle

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

This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

 Geometric Constructions with Triangles
Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle Video Transcript: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle

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

This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

 Geometric Constructions with Triangles
Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Angle Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Angle Video Tutorial: Desmos Geometry Exploration: Classifying Triangles by Angle

Topic

Geometry

Description

The video classifies triangles by their angles, highlighting acute, right, and obtuse triangles. Using Desmos, viewers construct and manipulate triangles to understand these categories. Key terms include equiangular, isosceles, and base angles. Applications involve creating different types of triangles and analyzing their angle properties.

 Definition of a Triangle and Geometric Constructions with Triangles
Video Tutorial: Desmos Geometry Exploration: Triangle Basics Video Tutorial: Desmos Geometry Exploration: Triangle Basics Video Tutorial: Desmos Geometry Exploration: Triangle Basics

Topic

Geometry

Description

Triangles are defined as three-sided closed figures with internal angles summing to 180°. The video demonstrates creating triangles with Desmos tools and exploring their properties. Key terms include vertices, line segments, and angles. Applications include constructing and measuring triangles to verify their angle sums.

 Definition of a Triangle and Geometric Constructions with Triangles
VIDEO: Geometry Applications: Triangles VIDEO: Geometry Applications: Triangles VIDEO: Geometry Applications: Triangles

Topic

Triangles

 Definition of a Triangle and Applications of Triangles
VIDEO: Geometry Applications: Triangles, Segment 1: Introduction VIDEO: Geometry Applications: Triangles, 1 VIDEO: Geometry Applications: Triangles, 1

Topic

Triangles

Description

This video introduces the importance of triangles in architecture and structural design. It highlights the use of triangles in structures like the Bank of China Tower in Hong Kong, noting their ability to provide strength and stability. The video focuses on the role of triangles in reinforcing skyscrapers to withstand strong winds, especially during typhoon seasons. Key vocabulary includes architectural support, triangular base, and stability. The video sets up a foundation for exploring how triangle properties are applied in real-world contexts.

 Definition of a Triangle and Applications of Triangles
VIDEO: Geometry Applications: Triangles, Segment 2: Triangles VIDEO: Geometry Applications: Triangles, 2 VIDEO: Geometry Applications: Triangles, 2

Topic

Triangles

 Applications of Triangles
VIDEO: Geometry Applications: Triangles, Segment 3: Right Triangles VIDEO: Geometry Applications: Triangles, 3 VIDEO: Geometry Applications: Triangles, 3

Topic

Triangles

 Applications of Triangles and Definition of a Triangle
VIDEO: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle VIDEO: Ti-Nspire Mini-Tutorial, Video 38 VIDEO: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle

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.

 Geometric Constructions with Triangles
VIDEO: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle VIDEO: Ti-Nspire Mini-Tutorial, Video 51 VIDEO: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle

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.

 Geometric Constructions with Triangles
VIDEO: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle VIDEO: Ti-Nspire Mini-Tutorial, Video 52 VIDEO: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle

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.

 Geometric Constructions with Triangles