Illustrative Math Alignment: Grade 8 Unit 8

Overview

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.

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.

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. .

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. .

Topic

Triangles

Topic

Triangles

Topic

Triangles

Topic

Triangles

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. .

Related Resources

Video Transcripts

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 

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.

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.

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.

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.

Library of Instructional Resources

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

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.

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

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

Related Resources

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.

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

Related Resources

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

Related Resources

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

Related Resources

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

Related Resources

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

Related Resources

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Topic

Geometry Basics

Description

This image provides an example of a scalene acute triangle, demonstrating how triangles can be classified by both their sides and angles. It helps students understand that triangles can belong to multiple categories simultaneously, deepening their comprehension of triangle geometry.

Using math clip art to showcase specific examples is particularly effective in geometry education. Teachers can use this image to illustrate how a triangle can be both scalene (all sides of different lengths) and acute (all angles less than 90 degrees) at the same time.

Topic

Geometry Basics

Description

This image showcases an example of a obtuse right triangle, illustrating how triangles can be classified by both their sides and angles. It helps students understand that triangles can belong to multiple categories simultaneously, deepening their comprehension of triangle geometry.

Using math clip art to present specific examples is particularly effective in geometry education. Teachers can use this image to demonstrate how a triangle can be both scalene (all sides of different lengths) and right-angled (one angle measuring exactly 90 degrees) at the same time.