Understanding Triangles: A Comprehensive Guide to Their Classification and Properties

• Equilateral Triangle:
  • All three sides are of equal length. All three angles measure \(60^\circ\).
  • Two sides are of equal length. The angles opposite these equal sides are also equal.
  • No sides are of equal length. None of the angles is equal.

• Acute Triangle:
  • All three angles are less than \(90^\circ\).
  • One angle measures exactly \(90^\circ\).
  • One angle measures more than \(90^\circ\).

Examples:

Practice Questions:

1. Classify a triangle with angles measuring \(80^\circ\), \(60^\circ\), and \(40^\circ\).
2. What type of triangle has sides measuring \(6 \text{cm}\), \(6 \text{cm}\), and \(6 \text{cm}\)?
3. Identify a triangle with one angle measuring \(100^\circ\) and the remaining two angles totaling \(80^\circ\).

1. Acute Triangle.
2. Equilateral Triangle.
3. Obtuse Triangle.