Summary of Classification of Shapes

Goals

1. Classify polygons based on the number of their sides (triangles and quadrilaterals).

2. Identify various types of triangles by examining their sides and angles.

3. Recognize equilateral, equiangular, and regular polygons.

Contextualization

Polygons are a part of our world in so many ways. From the buildings we call home to the intricate designs of bridges and vehicles, being able to classify geometric shapes is a vital skill. Grasping how to identify and categorize these shapes not only supports our math skills but is also essential in careers like architecture, civil engineering, and graphic design. For instance, triangles are often used in construction due to their inherent strength and stability, while quadrilaterals can be seen in common features like windows and doors.

Subject Relevance

To Remember!

Classification of Triangles by Sides

Triangles can be sorted into three categories based on their sides: equilateral, isosceles, and scalene. An equilateral triangle features three equal sides, an isosceles triangle has two equal sides, and a scalene triangle has all sides of different lengths.

• Equilateral Triangle: All sides are equal.

• Isosceles Triangle: Two sides are equal.

• Scalene Triangle: All sides are different.

Classification of Triangles by Angles

We can also classify triangles by the measure of their angles: acute, right, and obtuse. An acute triangle has all angles under 90 degrees, a right triangle has one angle exactly 90 degrees, and an obtuse triangle has one angle over 90 degrees.

• Acute Triangle: All angles are less than 90°.

• Right Triangle: Includes one 90° angle.

• Obtuse Triangle: Has one angle greater than 90°.

Classification of Quadrilaterals

Quadrilaterals are shapes with four sides and can be classified in several forms, including squares, rectangles, rhombuses, parallelograms, and trapezoids. Each type has its own unique properties regarding sides and angles.

• Square: All sides and angles are equal.

• Rectangle: Opposite sides are equal and angles are right.

• Rhombus: All sides are equal, but angles may not be right.

• Parallelogram: Opposite sides and angles are equal.

• Trapezoid: At least one pair of sides is parallel.

Equilateral, Equiangular, and Regular Polygons

Polygons can also be categorized based on their sides and angles. Equilateral polygons have all sides equal, equiangular polygons have all angles equal, and regular polygons have both equal sides and angles.

• Equilateral: All sides are equal.

• Equiangular: All angles are equal.

• Regular: All sides and angles are equal.

Practical Applications

• Architecture: Implementing triangles in roof designs to enhance stability.

• Civil Engineering: Crafting bridges that use polygonal shapes for effective weight distribution.

• Graphic Design: Crafting logos and geometric patterns using regular polygons for visual appeal.

Key Terms

• Polygon: A closed geometric figure made up of line segments.

• Equilateral Triangle: A triangle with all sides equal.

• Isosceles Triangle: A triangle with two sides equal.

• Scalene Triangle: A triangle with all sides different.

• Acute Triangle: A triangle with all angles less than 90°.

• Right Triangle: A triangle with one 90° angle.

• Obtuse Triangle: A triangle with one angle greater than 90°.

• Square: A quadrilateral with all sides and angles equal.

• Rectangle: A quadrilateral with opposite sides equal and right angles.

• Rhombus: A quadrilateral with all sides equal, but non-right angles.

• Parallelogram: A quadrilateral with equal opposite sides and angles.

• Trapezoid: A quadrilateral with at least one pair of parallel sides.

• Equilateral: A polygon with all sides equal.

• Equiangular: A polygon with all angles equal.

• Regular Polygon: A polygon with equal sides and angles.

Questions for Reflections

• How does classifying polygons impact the stability and practicality of a structure?

• In what ways is polygon knowledge advantageous in careers such as architecture and engineering?

• What challenges did you face when classifying polygons, and how did you resolve them?

Innovative Polygon Challenge

For this mini-challenge, you’ll use your newfound knowledge to embark on a creative project incorporating polygons.

Instructions

• Form pairs or groups of three.

• Grab some paper and pens to sketch a creative object or structure that includes at least three different types of polygons (both triangles and quadrilaterals).

• Identify each polygon used in your drawing by their sides and angles.

• Discuss how your selected polygons affect the stability and functionality of your creation.

• Present your project to the class, focusing on the classifications of the polygons and their practical applications.