1. Classification by Sides:

• Equilateral Triangle:
  • Description: All three sides are equal, and all three interior angles measure 60°.
  • Key Feature: Symmetrical in every way; all angles and sides are congruent.

• Isosceles Triangle:
  • Description: Two sides are of equal length, and the angles opposite these sides are equal.
  • Key Feature: Often has two equal angles, making it visually symmetrical across one axis.

• Scalene Triangle:
  • Description: All three sides have different lengths, and all three angles are different.
  • Key Feature: No symmetry in sides or angles.

2. Classification by Angles:

• Acute Triangle:
  • Description: All three interior angles are less than 90°.
  • Key Feature: The sum of the three acute angles still equals 180°, but each individual angle is small.

• Right-Angled Triangle:
  • Description: One of the angles is exactly 90° (a right angle).
  • Key Feature: The Pythagorean theorem applies, where the square of the hypotenuse (longest side) equals the sum of the squares of the other two sides: (a^2 + b^2 = c^2).

• Obtuse Triangle:
  • Description: One of the angles is greater than 90°.
  • Key Feature: The obtuse angle gives the triangle a wider, flatter shape.

3. Sum of Interior Angles:

• In any triangle, the sum of the interior angles always equals 180°.
• Example: For an isosceles triangle with two equal angles of 45°, the third angle will be 90° (since 45° + 45° = 90°, and 180° – 90° = 90°).