Introduction to Triangles

Introduction to Triangles

• A triangle is defined as a simple closed curve that consists of three line segments.
• Each triangle has three vertices, three sides, and three angles.
• For triangle ABC:
  • Sides: AB, BC, CA
  • Angles: ∠BAC, ∠ABC, ∠BCA
• The side opposite vertex A is denoted as BC.

Classification of Triangles

• Triangles can be classified based on:
  • Sides:
    • Scalene (all sides different)
    • Isosceles (two sides equal)
    • Equilateral (all sides equal)
  • Angles:
    • Acute-angled (all angles less than 90°)
    • Obtuse-angled (one angle greater than 90°)
    • Right-angled (one angle exactly 90°)

Medians of a Triangle

• A median of a triangle connects a vertex to the midpoint of the opposite side.
• Example: For triangle ABC, if D is the midpoint of side BC, then AD is a median.
• Every triangle has three medians.

Altitudes of a Triangle

• An altitude is a segment from a vertex perpendicular to the opposite side (the base).
• For triangle ABC, the altitude from vertex A to side BC is represented by segment AL.
• A triangle can have three altitudes, one from each vertex.

Discussion Points

• Students are prompted to discuss characteristics of triangles, including the number of medians and altitudes.
• Visual models and paper-cut experiments can aid understanding of triangle properties.
• Practicing the identification of triangle elements reinforces learning through application.