Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 8

Pythagorean Theorem and Irrational Numbers

Lesson 8: A Proof of the Pythagorean Theorem

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Examples Math Examples Collection: Right Triangles

Overview

The Media4Math collection on Right Triangles offers a comprehensive set of examples designed to enhance students' understanding of this fundamental geometric concept. These examples cover a wide range of skills, including applying the Pythagorean theorem, using trigonometric ratios, and solving real-world problems involving right triangles.

Right Triangles
Theorems Collection Math Definitions Collection: Geometry Theorems and Postulates

Overview

This collection aggregates all the definition image cards around the topic of Theorems and Postulates terms and vocabulary. There are a total of 18 terms. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

 

 

Definition of a Triangle, Definition of an Angle, Right Triangles and Definition of a Line
Math in the News Math in the News Collection: Applications of Exponential Functions

Overview

This is a collection of Math in the News stories that focus on the topic of Exponential Functions.

 

 

 
Applications of Exponential and Logarithmic Functions, Applications of Linear Functions, Data Analysis and Sequences
Math in the News Math in the News Collection: Business Math

Overview

This is a collection of issues of Math in the News that deal with business applications.

 

 

 
Applications of Exponential and Logarithmic Functions, Data Analysis and Volume
Animated Math Clip Art Animated Math Clip Art--3D Geometry--Rotating a Triangle to Form a Cone Rotating a Triangle to Form a Cone

Topic

3D Geometry

Description

This animation shows how rotating a triangle around one of its sides creates a cone. It's a powerful visualization of how 2D shapes can generate 3D objects through rotation.

Animated math clip art like this is crucial for teaching as it helps students visualize the formation of cones. Teachers can use this to introduce concepts of volume and surface area of cones, as well as topics in calculus related to solids of revolution.

Cones
Closed Captioned Video: TI-Nspire Mini-Tutorial: Constructing the Circumcenter of a Triangle Closed Captioned Video: Circumcenter of a Triangle Closed Captioned Video: 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. This Mini-Tutorial Video includes a worksheet. .

Geometric Constructions with Triangles
Closed Captioned Video: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle Closed Captioned Video: Circumscribing a Circle-Triangle Closed Captioned Video: Circumscribing a Circle-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. This Mini-Tutorial Video includes a worksheet. .

Geometric Constructions with Triangles
Closed Captioned Video: Geometry Applications: Triangles Closed Captioned Video: Geometry Applications: Triangles Closed Captioned Video: Geometry Applications: Triangles

Topic

Triangles

Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Geometry Applications: Triangles, Segment 1: Introduction Closed Captioned Video: Geometry Applications: Triangles, 1 Closed Captioned Video: Geometry Applications: Triangles, 1

Topic

Triangles

Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Geometry Applications: Triangles, Segment 2: Triangles Closed Captioned Video: Geometry Applications: Triangles, 2 Closed Captioned Video: Geometry Applications: Triangles, 2

Topic

Triangles

Definition of a Triangle and Applications of Triangles
Closed Captioned Video: Geometry Applications: Triangles, Segment 3: Right Triangles Closed Captioned Video: Geometry Applications: Triangles, 3 Closed Captioned Video: Geometry Applications: Triangles, 3

Topic

Triangles

Definition of a Triangle and Applications of Triangles
Closed Captioned Video: TI-Nspire Mini-Tutorial: Constructing the Orthocenter of a Triangle Closed Captioned Video: Orthocenter of a Triangle Closed Captioned Video: 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. This Mini-Tutorial Video includes a worksheet. .

This is part of a collection of closed captioned videos on various math topics. To see the complete collection of the videos, click on this link. Note: The download is Media4Math's guide to closed captioned videos.

Related Resources

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

Video Transcripts

This video has a transcript available. To see the complete collection of video transcripts, click on this link.
Geometric Constructions with Triangles
Distance Formula. The equation used to find the distance between two points, given their coordinates. Definition--Geometry Basics--Distance Formula Distance Formula

Topic

Geometry Basics

Definition

The distance formula is used to determine the distance between two points in a coordinate plane.

Description

The distance formula is derived from the Pythagorean Theorem and is given by 

The Distance Formula
Definition--Geometry Basics--Perpendicular Bisector Definition--Geometry Basics--Perpendicular Bisector Perpendicular Bisector

Topic

Geometry Basics

Definition

A line that divides a segment into two equal parts at a 90-degree angle.

Description

A perpendicular bisector is a line that divides a line segment into two equal parts at a right angle (90 degrees). This concept is essential in geometry for constructing and analyzing geometric shapes. For example, the perpendicular bisectors of the sides of a triangle intersect at the circumcenter, which is equidistant from all vertices of the triangle. Understanding perpendicular bisectors is crucial for solving problems related to symmetry and geometric constructions.

Definition of a Line
Definition--Theorems and Postulates--Converse of the Pythagorean Theorem Definition--Theorems and Postulates--Converse of the Pythagorean Theorem Definition--Theorems and Postulates--Converse of the Pythagorean Theorem

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

Right Triangles
Definition--Theorems and Postulates--HL Theorem Definition--Theorems and Postulates--HL Theorem Definition--Theorems and Postulates--HL Theorem

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

Right Triangles
Definition--Theorems and Postulates--Perpendicular Bisector Theorem Definition--Theorems and Postulates--Perpendicular Bisector Theorem Definition--Theorems and Postulates--Perpendicular Bisector Theorem

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

Definition of a Line
Definition--Theorems and Postulates--Pythagorean Theorem Definition--Theorems and Postulates--Pythagorean Theorem Definition--Theorems and Postulates--Pythagorean Theorem

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

Right Triangles
Google Earth Video Geometry Applications, Triangles, Segment 1, Introduction 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.

Applications of Triangles and Definition of a Triangle
INSTRUCTIONAL RESOURCE: Math Examples--Right Triangles INSTRUCTIONAL RESOURCE: Math Examples 46 INSTRUCTIONAL RESOURCE: Math Examples--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 math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Right Triangles
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Constructing an Isosceles Triangle INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Constructing an Isosceles Triangle

In this Slide Show, we show how to construct an isosceles triangle. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

Definition of a Triangle and Geometric Constructions with Triangles
INSTRUCTIONAL RESOURCE: TI-Nspire App Activity: Constructing an Isosceles Triangle INSTRUCTIONAL RESOURCE: TI-Nspire App Activity: Constructing an Isosceles Triangle

In this Slide Show, learn how to use the TI-Nspire App to construct an isosceles triangle. Note: The download is a PPT file.

Definition of a Triangle and Geometric Constructions with Triangles
Interactive Crossword Puzzle--Quadrilaterals Interactive Crossword Puzzle--Quadrilaterals Interactive Crossword Puzzle--Quadrilaterals

This interactive crossword puzzle tests knowledge of key terms on the topic of quadrilaterals.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Quadrilateral
Interactive Crossword Puzzle--Triangles Interactive Crossword Puzzle--Triangles Interactive Crossword Puzzle--Triangles

This interactive crossword puzzle tests knowledge of key terms on the topic of triangles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Interactive Math Game, Math Riddles--Triangles Interactive Math Game: Math Riddles--Triangles Interactive Math Game: Math Riddles--Triangles

In this Math Riddles Game, have your students review vocabulary around the topic of triangles. The Math Riddles games are useful for practicing: Math Vocabulary, Key Concepts, Critical Thinking.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Interactive Word Search Puzzle--Triangles, Puzzle 1 Interactive Word Search Puzzle--Triangles, Puzzle 1 Interactive Word Search Puzzle--Triangles, Puzzle 1

Solve an interactive word search puzzle on the topic of Triangles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Interactive Word Search Puzzle--Triangles, Puzzle 2 Interactive Word Search Puzzle--Triangles, Puzzle 2 Interactive Word Search Puzzle--Triangles, Puzzle 2

Solve an interactive word search puzzle on the topic of Triangles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Interactive Word Search Puzzle--Triangles, Puzzle 3 Interactive Word Search Puzzle--Triangles, Puzzle 3 Interactive Word Search Puzzle--Triangles, Puzzle 3

Solve an interactive word search puzzle on the topic of Triangles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Interactive Word Search Puzzle--Triangles, Puzzle 4 Interactive Word Search Puzzle--Triangles, Puzzle 4 Interactive Word Search Puzzle--Triangles, Puzzle 4

Solve an interactive word search puzzle on the topic of Triangles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Interactive Word Search Puzzle--Triangles, Puzzle 5 Interactive Word Search Puzzle--Triangles, Puzzle 5 Interactive Word Search Puzzle--Triangles, Puzzle 5

Solve an interactive word search puzzle on the topic of Triangles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 01 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 01 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 01

Topic

Geometry Basics

Description

This math clip art image serves as the title card for a series on classifying triangles by angles. It reads "Classifying Triangles by Angle." This image is part of a comprehensive set designed to teach students about the different types of triangles based on their angles.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 02 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 02 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 02

Topic

Geometry Basics

Description

This math clip art image is the second in a series about categorizing angles in triangles. It depicts a triangle labeled ABC, illustrating the fundamental principle that a triangle includes three angles whose sum is 180 degrees. This key concept in geometry is visually represented, providing students with a clear understanding of this crucial property of triangles.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 03 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 03 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 03

Topic

Geometry Basics

Description

This math clip art image is the third in a series about categorizing angles in triangles. It showcases an acute triangle, demonstrating that an acute triangle consists of three acute angles. The image clearly illustrates the defining characteristic of an acute triangle, where all three angles are less than 90 degrees.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 04 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 04 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 04

Topic

Geometry Basics

Description

This math clip art image is the fourth in a series about categorizing angles in triangles. It presents a right triangle, illustrating that a right triangle consists of one 90-degree angle and two acute angles. The image clearly demonstrates the defining characteristic of a right triangle, emphasizing the 90-degree angle and the two acute angles that complete the 180-degree sum.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 05 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 05 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 05

Topic

Geometry Basics

Description

This math clip art image is the fifth in a series about categorizing angles in triangles. It showcases an obtuse triangle, demonstrating that an obtuse triangle consists of one obtuse angle and two acute angles. The image clearly illustrates the defining characteristic of an obtuse triangle, highlighting the one angle that is greater than 90 degrees and the two acute angles that complete the 180-degree sum.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 06 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 06 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 06

Topic

Geometry Basics

Description

This math clip art image is the sixth in a series about categorizing angles in triangles. It depicts an isosceles triangle, illustrating that an isosceles triangle has two congruent acute angles. The image clearly demonstrates the defining characteristic of an isosceles triangle, highlighting the two equal angles and their corresponding equal sides.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 07 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 07 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 07

Topic

Geometry Basics

Description

This math clip art image is the seventh in a series about categorizing angles in triangles. It showcases an equiangular triangle, demonstrating that an equiangular triangle consists of three acute angles of 60 degrees each. The image clearly illustrates the defining characteristic of an equiangular triangle, highlighting that all three angles are equal and measure 60 degrees.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 08 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 08 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 08

Topic

Geometry Basics

Description

This math clip art image is the eighth in a series about categorizing angles in triangles. It presents a comprehensive table that summarizes the three categories of triangles. The image provides a clear overview of the different types of triangles classified by their angles, including acute, right, and obtuse triangles, along with their defining characteristics.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 09 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 09 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 09

Topic

Geometry Basics

Description

This math clip art image, which is the ninth in the series about categorizing triangles by angles, showcases real-world examples of acute triangles. It features a Yield sign and a No Passing Zone sign, both of which are shaped like acute triangles. These examples illustrate how acute triangles, which consist of three angles that are all less than 90 degrees, can be found in everyday objects. The sharp angles of these signs not only serve a functional purpose in guiding drivers but also provide a clear visual representation of acute triangles in a real-world context.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 10 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 10 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 10

Topic

Geometry Basics

Description

This math clip art image is the tenth in the series about categorizing triangles by angles, depicting a real-world example of a right triangle. It shows the right triangle portion of a truss, which effectively illustrates the structural applications of right triangles in engineering and construction. Right triangles consist of one 90-degree angle and two acute angles, collaborating harmoniously to provide strength and stability in various designs.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 11 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 11 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 11

Topic

Geometry Basics

Description

This math clip art image, which is the eleventh in the series about categorizing triangles by angles, illustrates a real-world example of an obtuse triangle. It depicts the roof of a house, showcasing the triangular shape it forms, where one angle is greater than 90 degrees, categorizing it as an obtuse triangle. This example emphasizes the significance of obtuse triangles in architecture and design, highlighting how these shapes provide aesthetic and structural benefits.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying TriAngles, Image by Angles, Image 12 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 12 Math Clip Art--Geometry Basics--Classifying Triangles by Angles 12

Topic

Geometry Basics

Description

This math clip art image is the twelfth in the series about categorizing triangles by angles, depicting a real-world example of an equilateral triangle. It shows a portion of a truss, illustrating how equilateral triangles, which have all three angles equal to 60 degrees, are utilized in construction for their symmetrical properties. This example underscores the significance of equilateral triangles in design, providing both aesthetic appeal and structural integrity.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 01 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 01 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 01

Topic

Geometry Basics

Description

This image is part of a series about categorizing triangles, serving as a title card for the collection. It introduces the concept of "Classifying Triangles by Side," setting the stage for a comprehensive exploration of triangle types. The use of clear, visually appealing math clip art is crucial in geometry education, as it helps students visualize abstract concepts and makes learning more engaging.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 02 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 02 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 02

Topic

Geometry Basics

Description

This image illustrates a fundamental concept in triangle geometry: every triangle consists of three sides, each with its own specific length. It's an essential starting point for understanding how triangles can be classified based on their sides.

Math clip art like this is invaluable in geometry education as it provides a clear, visual representation of abstract concepts. Teachers can use this image to introduce the basic definition of a triangle and as a foundation for more complex classifications.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 03 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 03 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 03

Topic

Geometry Basics

Description

This image introduces the concept of a scalene triangle, which is characterized by having three sides of different lengths. It's an important classification in triangle geometry and helps students understand the diversity of triangle types.

Using math clip art in this context allows for clear visual representation of the unique property of scalene triangles. Teachers can use this image to help students identify and understand this specific triangle classification.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 04 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 04 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 04

Topic

Geometry Basics

Description

This image introduces the concept of an isosceles triangle, which is defined by having two sides that are congruent or equal in length. It's a key classification in triangle geometry and helps students understand another important type of triangle.

Math clip art like this is crucial in geometry education as it provides a clear visual representation of the unique property of isosceles triangles. Teachers can use this image to help students identify and understand this specific triangle classification.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 05 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 05 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 05

Topic

Geometry Basics

Description

This image introduces the concept of an equilateral triangle, which is characterized by having all three sides congruent or equal in length. It's a significant classification in triangle geometry and represents a special case of triangle symmetry.

Using math clip art in this context allows for a clear visual representation of the unique property of equilateral triangles. Teachers can use this image to help students identify and understand this specific triangle classification and its implications for angle measures.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 06 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 06 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 06

Topic

Geometry Basics

Description

This image expands on the concept of isosceles triangles by highlighting an important property: an isosceles triangle has two congruent acute angles. This information helps students understand the relationship between side lengths and angles in triangles.

Math clip art like this is invaluable in geometry education as it visually demonstrates the connection between a triangle's sides and its angles. Teachers can use this image to deepen students' understanding of isosceles triangles and introduce the concept of angle-side relationships in triangles.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 07 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 07 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 07

Topic

Geometry Basics

Description

This image presents a table that explores various combinations of triangle classifications. It helps students understand how different triangle types can be related and combined, deepening their comprehension of triangle geometry.

Using math clip art in this tabular format is particularly effective for organizing and comparing different triangle classifications. Teachers can use this image to guide students through the various combinations and discuss the relationships between different triangle types.

Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides, Image 08 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 08 Math Clip Art--Geometry Basics--Classifying Triangles by Sides 08

Topic

Geometry Basics

Description

This image presents a table that illustrates which types of triangles are mathematically possible and which are not. It helps students understand the constraints and possibilities within triangle classifications, deepening their comprehension of triangle geometry.

Using math clip art in this tabular format is particularly effective for organizing and comparing different triangle types. Teachers can use this image to guide students through the various combinations and discuss why some are permitted while others are not.

Definition of a Triangle