Introduction to Triangles

Study Notes

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.

Description

This quiz covers the fundamental concepts of triangles, including their definitions, classifications based on sides and angles, and the properties of medians and altitudes. Test your understanding of different types of triangles and their characteristics in this informative quiz.