Illustrative Math Alignment: Grade 8 Unit 8

Pythagorean Theorem and Irrational Numbers

Lesson 6: Finding Side Lengths of Triangles

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 09	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 09 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.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 10	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 10 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.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 11	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 11 Topic Geometry Basics Description This image presents an example of an isosceles right 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, enhancing their comprehension of triangle geometry. Using math clip art to illustrate specific examples is particularly effective in geometry education. Teachers can use this image to show how a triangle can be both isosceles (two sides of equal length) and acute (all angles less than 90 degrees) at the same time.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 12	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 12 Topic Geometry Basics Description This image showcases an example of an isosceles acute 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 isosceles (two sides of equal length) and obtuse (one angle measuring more than 90 degrees) at the same time.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 13	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 13 Topic Geometry Basics Description This image presents an example of an isosceles obtuse 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, enhancing their comprehension of triangle geometry. Using math clip art to illustrate specific examples is particularly effective in geometry education. Teachers can use this image to show how a triangle can be both isosceles (two sides of equal length) and right-angled (one angle measuring exactly 90 degrees) at the same time.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 14	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 14 Topic Geometry Basics Description This image showcases an example of an equilateral right triangle, illustrating a special case in triangle classification. It helps students understand the unique properties of equilateral triangles and their relationship to acute angles, 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 all equilateral triangles are necessarily acute, with each angle measuring exactly 60 degrees.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 15	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 15 Topic Geometry Basics Description This image showcases an example of an equilateral acute triangle, illustrating a special case in triangle classification. It helps students understand the unique properties of equilateral triangles and their relationship to acute angles, 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 all equilateral triangles are necessarily acute, with each angle measuring exactly 60 degrees.	Definition of a Triangle
Math Clip Art--Geometry Basics--Classifying Triangles by Sides 16	Math Clip Art--Geometry Basics--Classifying Triangles by Sides 16 Topic Geometry Basics Description This image presents a comprehensive summary table of triangles classified by their sides. It serves as an essential reference tool, helping students understand the various types of triangles based on their side lengths and how these classifications relate to angular properties. 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 classifications and discuss the relationships between side lengths and angle measures in triangles.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 01	Math Clip Art--Geometry Basics--Triangle Basics 01 Topic Geometry Basics Description This image is part of a comprehensive series covering triangle basics, designed to enhance geometry education using clip art. This is the title card, "Triangle Basics."	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 02	Math Clip Art--Geometry Basics--Triangle Basics 02 Topic Geometry Basics Description This image is part of a series focusing on triangle basics, designed to enhance geometry education through visual aids. The illustration presents a simple triangle, emphasizing that it is a closed figure with three straight sides. This fundamental definition is crucial for students to understand before delving deeper into triangle properties and theorems.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 03	Math Clip Art--Geometry Basics--Triangle Basics 03 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a triangular shape that is not closed, emphasizing that it does not meet the definition of a triangle. This example helps students understand the importance of closure in defining geometric shapes.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 04	Math Clip Art--Geometry Basics--Triangle Basics 04 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a circular sector shape, emphasizing that while it is a closed figure with three sides, it is not a triangle because not all sides are straight. This example helps students understand the importance of straight sides in defining triangles.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 05	Math Clip Art--Geometry Basics--Triangle Basics 05 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a triangle, emphasizing that it has three sides made up of three line segments. This fundamental concept is crucial for students to understand as they begin their study of triangles and their properties.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 06	Math Clip Art--Geometry Basics--Triangle Basics 06 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a triangle formed from rays and lines, expanding students' understanding of how triangles can be constructed. This concept introduces more advanced geometric ideas and helps bridge the gap between basic shapes and complex geometric figures.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 07	Math Clip Art--Geometry Basics--Triangle Basics 07 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a triangle with labeled endpoints, introducing the concept of vertex labeling in geometry. This fundamental skill is crucial for students as they progress to more complex geometric problems and proofs.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 08	Math Clip Art--Geometry Basics--Triangle Basics 08 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a labeled triangle, emphasizing how to use these labels to define the sides of the triangle. This concept is fundamental for students as they learn to describe and analyze triangles in more detail.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 09	Math Clip Art--Geometry Basics--Triangle Basics 09 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration highlights that a triangle consists of three angles, a fundamental property that defines this shape. This concept is crucial for students to understand as they begin to explore more complex properties of triangles.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 10	Math Clip Art--Geometry Basics--Triangle Basics 10 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows a triangle ABC, demonstrating how the endpoints (vertices) can be used to label both the sides and angles of the triangle. This concept is fundamental for students as they learn to describe and analyze triangles in more detail.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 11	Math Clip Art--Geometry Basics--Triangle Basics 11 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows triangle ABC, further emphasizing how the endpoints (vertices) can be used to label both the sides and angles of the triangle. This reinforces the concept introduced in the previous image and helps students become more comfortable with triangle notation.	Definition of a Triangle
Math Clip Art--Geometry Basics--Triangle Basics 12	Math Clip Art--Geometry Basics--Triangle Basics 12 Topic Geometry Basics Description This image is part of a series on triangle basics, designed to enhance geometry education through visual aids. The illustration shows triangle ABC, highlighting one of the most fundamental properties of triangles: the sum of their interior angles is always 180 degrees. This concept is crucial for students to understand as it forms the basis for many other geometric principles and proofs.	Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 1	Math Clip Art--Kite Shape 1 Topic Geometry Concepts Description This image features a kite shape, in this case a circular one. Ordinarily a kite is a quadrilateral with two pairs of adjacent equal-length sides. The diagonals intersect at right angles, and one diagonal bisects the other, creating a symmetrical shape. Kite shapes are important in geometry for understanding properties like symmetry, area, and perimeter. They are used in various mathematical applications, including tiling and design. Teacher's Script: "Examine this kite. What makes it a kite in the everyday understanding of it? Is it a kite in geometric terms?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 10	Math Clip Art--Kite Shape 10 Topic Geometry Concepts Description This image features a kite shape, a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures. Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.	Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 11	Math Clip Art--Kite Shape 11 Topic Geometry Concepts Description This image depicts a kite shape, characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique. Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture. Teacher's Script: "Look at this kite shape. How do its symmetrical properties and intersecting diagonals help us understand its geometry? What are some mathematical concepts you can explore using kite shapes?"	Definition of a Polygon and Definition of a Triangle

Illustrative Math Alignment: Grade 8 Unit 8

Pythagorean Theorem and Irrational Numbers

Lesson 6: Finding Side Lengths of Triangles

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