Common Core: High School - Geometry

Explore the principles and applications of geometry, including shapes, theorems, and real-world problem-solving.

Foundations of GeometryTriangles and Their PropertiesQuadrilaterals and Polygons
Congruence and SimilarityThe Pythagorean TheoremCircles and Their Properties
Geometry in ArchitectureGeometry in Art and DesignGeometry in Everyday Problem-Solving
Drawing and Visualizing ProblemsBreaking Problems into Steps
Foundations of Geome...Triangles and Their ...Quadrilaterals and P...Congruence and Simil...The Pythagorean Theo...Circles and Their Pr...Geometry in Architec...Geometry in Art and ...Geometry in Everyday...Drawing and Visualiz...Breaking Problems in...
Basic Concepts

Quadrilaterals and Polygons

Exploring Polygons

Polygons are closed shapes with straight sides. Quadrilaterals are polygons with four sides, but polygons can have any number of sides.

Types of Quadrilaterals

  • Rectangle: Opposite sides equal; angles are 90°.
  • Square: All sides and angles equal.
  • Parallelogram: Opposite sides are parallel and equal.
  • Trapezoid: Only one pair of sides is parallel.

Properties of Polygons

  • The sum of interior angles of an \(n\)-sided polygon is \((n-2) \times 180^\circ\).
  • Polygons are found everywhere, from honeycombs (hexagons) to stop signs (octagons)!

Why Study Polygons?

Polygons help us understand tiling, art, architecture, and even computer graphics for games and animation.

Examples

  • A soccer field is shaped like a rectangle.

  • Windows often have a square or rectangular design.

In a Nutshell

Polygons, especially quadrilaterals, are key to understanding many real-world shapes and structures.

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Congruence and Similarity