Illustrative Math Alignment: Grade 8 Unit 8

Topic

Polygons

Definition

A regular polygon is a polygon with all sides and angles equal.

Description

Regular polygons play a significant role in geometry due to their symmetrical properties and uniformity. These shapes are defined by having all sides of equal length and all interior angles of equal measure. This symmetry makes regular polygons a fundamental subject of study in various fields of mathematics and applied sciences.

Topic

Polygons

Definition

Similar polygons are polygons that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

Description

In geometry, the concept of similar polygons is fundamental. Similar polygons maintain the same shape but can vary in size. This means that all corresponding angles between the two polygons are equal, and the lengths of corresponding sides are proportional. For instance, two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are in the same ratio.

Topic

Polygons

Definition

The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360°.

Description

The sum of exterior angles of a polygon is a fundamental concept in geometry that holds true for all polygons, regardless of their shape or number of sides. This property is crucial for understanding the nature of polygons and their relationship to circular motion. Exterior angles are formed by extending each side of the polygon and measuring the angle between this extension and the adjacent side.

Topic

Polygons

Definition

An interior angle of a polygon is an angle formed inside the polygon by two adjacent sides.

Topic

Polygons

Definition

A tessellation is a repeating pattern of geometric shapes that covers a plane without gaps or overlaps.

Description

Tessellations are fascinating geometric arrangements that play a significant role in both mathematics and art. They occur when a surface is completely covered by repeating shapes, leaving no gaps or overlaps. In geometry, tessellations demonstrate how certain shapes can fit together perfectly to create intricate patterns. The most common shapes used in tessellations are regular polygons, such as triangles, squares, and hexagons, due to their uniform angles and sides.

Topic

Polygons

Definition

A triangle is a polygon with three sides and three angles.

Description

Triangles are fundamental shapes in geometry, serving as the building blocks for many complex geometric figures and concepts. Their simplicity and versatility make them crucial in various mathematical and real-world applications. Triangles are classified based on their side lengths and angle measures, leading to categories such as equilateral, isosceles, and scalene triangles, as well as right, acute, and obtuse triangles.

Topic

Quadrilaterals

Definition

The area of a parallelogram is calculated by multiplying the base by the height.

Topic

Quadrilaterals

Definition

The area of a quadrilateral can be determined using various formulas depending on its type.

Topic

Quadrilaterals

Definition

The area of a quadrilateral can be determined using various formulas depending on its type.

Topic

Quadrilaterals

Definition

The area of a rectangle is computed as length times width.

Description

The area of a rectangle is a foundational concept in geometry, widely utilized in various real-world applications including furniture design and urban planning. The area is given by the formula A = length × width. Grasping this concept provides a basic understanding of spatial relationships essential in mathematics, which is vital for students to progress in their math education.

Topic

Quadrilaterals

Definition

The area of a rhombus can be found using the formula A = (d1 × d2)/2.

Description

The area of a rhombus, an intriguing type of quadrilateral, is essential in design and architecture. Utilizing the formula 

A = (d1 × d2)/2

where d1​ and d2  are the lengths of the diagonals, one can solve complex spatial problems. This concept illustrates the interplay between geometry and design, making it extremely relevant in math education.

Topic

Quadrilaterals

Definition

The area of a square is calculated as side length squared.

Description

The area of a square is fundamental in various fields such as mathematics and engineering. The formula is 

A = side2

demonstrating the square's properties and its applications in real-world contexts like floor planning and landscaping. Mastery of this concept is crucial for students to develop a comprehensive understanding of geometry within their math education.

Topic

Quadrilaterals

Definition

The area of a trapezoid is calculated using the formula 

Description

The area of a trapezoid is a significant concept in geometry, with applications in fields such as architecture and engineering. The formula for calculating the area is 

Topic

Quadrilaterals

Definition

Congruent quadrilaterals are quadrilaterals that have the same size and shape.

Description

The concept of congruent quadrilaterals is essential in geometry, as it helps in understanding the properties of shapes that are identical in form. This concept is used in various real-world applications, such as in design and construction, where it is important to ensure that components are congruent for structural integrity. Understanding congruence is crucial in math education as it lays the foundation for more advanced geometric concepts.

Topic

Quadrilaterals

Definition

The diagonals of a parallelogram bisect each other.

Description

The property of diagonals bisecting each other in a parallelogram is a key concept in geometry, illustrating the symmetry and balance within these shapes. This property is applied in various fields, such as engineering and architecture, where understanding the internal structure of shapes is crucial. Mastery of this concept is important in math education as it helps students understand the relationships between different parts of a shape.

Topic

Quadrilaterals

Definition

The diagonals of a quadrilateral are the line segments that connect opposite corners.

Description

The diagonals of a quadrilateral provide insights into the shape's symmetry and balance, which are important in both theoretical and practical applications. This concept is used in fields such as computer graphics and design, where understanding the internal structure of shapes is crucial. Understanding diagonals is a fundamental part of math education, as it helps students develop spatial reasoning skills.

Topic

Quadrilaterals

Definition

The diagonals of a rectangle are equal in length and bisect each other.

Description

The property of diagonals being equal and bisecting each other in a rectangle is a fundamental concept in geometry. This property is applied in various fields, such as architecture and engineering, where precision in measurements is crucial. Understanding this concept is important in math education as it helps students grasp the relationships between different parts of a shape and develop spatial reasoning skills.

Topic

Quadrilaterals

Definition

The diagonals of a trapezoid are line segments connecting the opposite corners.

Topic

Quadrilaterals

Definition

An inscribed square is a square drawn within a circle such that all four vertices of the square touch the circle.

Topic

Quadrilaterals

Definition

The sum of the interior angles of a quadrilateral is always 360 degrees.

Topic

Quadrilaterals

Definition

A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal.

Description

Kites are unique geometric figures that play a significant role in both theoretical and applied mathematics. The properties of kites are utilized in real-world applications, such as in design and computer graphics. Moreover, understanding kites enhances students' grasp of more advanced geometric properties and relationships, making this concept highly relevant in math education.

Topic

Quadrilaterals

Definition

A parallelogram is a quadrilateral with opposite sides that are equal and parallel.

Description

Parallelograms hold significant importance in both theoretical and applied mathematics. They are observed in various real-world situations such as architecture and engineering designs. Understanding the properties of parallelograms forms a foundation for more complex geometric concepts that students will encounter in their education, which highlights their relevance in mathematics teaching.

Topic

Quadrilaterals

Definition

The perimeter of a quadrilateral is the sum of the lengths of all its sides.

Description

Calculating the perimeter of a quadrilateral is a basic yet crucial learning objective in geometry. It finds application in everyday scenarios, such as fencing a yard or styling an outdoor space. This fundamental concept is pivotal for developing measurement skills within mathematics. Understanding how to determine the perimeter equips students with essential tools to solve more complex problems in their mathematical journey.

Topic

Quadrilaterals

Definition

A quadrilateral is a four-sided polygon characterized by its vertices and edges.

Description

Quadrilaterals are foundational shapes in geometry that underpin more advanced concepts. Utilizing quadrilaterals in both theoretical models and real-world applications, such as in architecture and design, exemplifies their significance. Grasping the properties of quadrilaterals helps students build essential reasoning skills necessary in various fields of math and science, emphasizing the need for a strong understanding of geometric principles.

Topic

Quadrilaterals

Definition

A rectangle is a quadrilateral with opposite sides equal and four right angles.

Description

Rectangles are one of the most common geometric shapes, greatly used across different domains including art, architecture, and various forms of design. Understanding the properties and applications of rectangles is crucial in math education as they form a basis for learning about more complex geometric shapes. Mastery of rectangles allows students to develop spatial understanding and problem-solving skills needed for more advanced math topics.

Topic

Quadrilaterals

Definition

A rhombus is a quadrilateral with all sides equal in length.

Description

The rhombus, with its unique properties, serves as an integral concept in geometry. Its applications span design and manufacturing industries, where equal lengths are essential. Assuring that students understand the rhombus furthers their grasp of geometric properties and relationships, underpinning more advanced learning in mathematics education.

Topic

Quadrilaterals

Definition

Similar quadrilaterals are quadrilaterals that have the same shape but different sizes.

Description

Understanding similar quadrilaterals profoundly impacts students' comprehension of proportional reasoning and geometric transformations. This concept finds applications in scaling models in architecture and art. Recognizing the properties of similarity aids students as they develop critical skills that are fundamental for success in later math courses, particularly in geometry and trigonometry.

Topic

Quadrilaterals

Definition

A square is a quadrilateral with all four sides of equal length and all four angles equal to 90 degrees.

Topic

Quadrilaterals

Definition

A trapezoid is a quadrilateral with at least one pair of parallel sides.

Description

The trapezoid is a versatile geometric shape with applications in various fields such as architecture, engineering, and art. Its defining feature is having one pair of parallel sides, which makes it useful for creating structures and designs that require stability and balance. Understanding trapezoids helps students grasp the concept of parallelism and its implications in geometry. This knowledge is vital for solving real-world problems and enhances students' overall mathematical proficiency.

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

Use this math game to review circles. This is a Memory-style game in which students must remember the location of pairs of identical images.

Related Resources

Use this math game to review polygons. This is a Memory-style game in which students must remember the location of pairs of identical images.

Related Resources

Use this math game to review quadrilaterals. This is a Memory-style game in which students must remember the location of pairs of identical images.

Related Resources

Use this math game to review triangles. This is a Memory-style game in which students must remember the location of pairs of identical images.

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.

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

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.