Classifying shapes by line and angle types
Classifying shapes by line and angle types involves organizing geometric figures based on their characteristics, such as the number of sides, angles, and other attributes. Shapes can be categorized as two-dimensional or three-dimensional, with two-dimensional shapes, or polygons, being made up of straight lines and angles. A polygon must have at least three sides, with triangles being the simplest form, consisting of three sides and angles. More complex classifications can include quadrilaterals, which have four sides and angles that sum to 360°. These can further be defined by the presence of parallel lines or congruent sides, leading to classifications such as parallelograms and squares. Angles play a crucial role in classification, with types including obtuse, right, and acute angles, while regular shapes feature congruent angles. Understanding these classifications not only helps learners grasp geometric concepts but is also vital in practical applications, such as product design and technology development, where the arrangement of shapes influences functionality and efficiency.
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Subject Terms
Classifying shapes by line and angle types
Shapes are figures in which lines, curves or both connect to make a closed figure. Closed figures can be either two dimensional or three dimensional. The two-dimensional shapes are flat planes or unraised figures. Many shapes have strong physical resemblances, and they can be classified by their similarities. Shapes that are two-dimensional and made of lines and angles are polygons.
Overview
Shapes can be classified using simple categories, such as the number of lines or angles, or more complex categories, such as attributes and properties. A polygon is a shape with straight sides, and at least three lines are required to form a polygon. A triangle, the simplest polygon, has three sides (lines) and three angles. Attributes are relative to the position of the lines and angles that make up the shape.
For example, quadrilaterals by definition have four sides with angles that add up to 360°. Quadrilaterals may include two sets of lines that are parallel (parallelograms), or have only one set of parallel sides or none at all. Line segments may also be congruent, that is, of equal length, as in a square, which has four congruent sides and four congruent angles.
Angles and vertices are attributes by which polygons may also be classified. Angles occur where two line segments intersect. Angles may be obtuse (greater than 90°), right (90°), or acute (less than 90°). Shapes with congruent angles are called regular and include rectangles (all angles are 90°) and pentagons (a five-sided figure with five 108° angles), for example.
Real-World Perspective
Classifications of geometric structures in math assist novice learners in organizing their knowledge and understanding of their environments. When using plane figures, it allows the developer of a product to better understand how all parts fit together to make the final product work as concisely as it should. When creating hardware for a technology device, understanding shapes, angles, and lines is critical whether it is creating space for a microchip or designing the lens of a retinal scanner.
Bibliography
Alonso, Orlando B., and Joseph Malkevitch. "Classifying Triangles and Quadrilaterals." The Mathematics Teacher 106.7 (2013): 541.
McKellar, Danica. Girls Get Curves. New York: Penguin, 2012.
Posamentier, Alfred S, and Robert L. Bannister. Geometry, Its Elements and Structure. Mineola, NY: Dover, 2014.
Salinas, Tracie McLemore, et al. "Exploring Quadrilaterals to Reveal Teachers' Use of Definitions: Results and Implications." Australian Senior Mathematics Journal 28.2 (2014): 50-59.