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

Triangles and Their Properties

All About Triangles

Triangles are three-sided polygons and play a huge role in geometry. They are classified by their side lengths and angles.

Types of Triangles

  • Equilateral: All sides and angles are equal.
  • Isosceles: Two sides (and their angles) are equal.
  • Scalene: All sides and angles are different.
  • Right Triangle: Has one 90° angle.

Triangle Properties

  • The sum of the angles in a triangle is always \(180^\circ\).
  • The longest side is opposite the largest angle.

Why Triangles Matter

Triangles are incredibly stable and used in structures like bridges and roofs. Understanding their properties helps in engineering, art, and even navigation!

Examples

  • Road signs often use equilateral triangles for stability.

  • A ramp can be modeled as a right triangle.

In a Nutshell

Triangles come in many shapes, but always have three angles adding up to 180°.

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Quadrilaterals and Polygons