Types of triangle?

1. Equilateral triangle: All three sides are of equal length and all three angles are equal (60 degrees).

2. Isosceles triangle: Two sides are of equal length and two angles are equal.

3. Scalene triangle: All three sides and angles are different.

4. Right triangle: One angle is a right angle (90 degrees).

5. Acute triangle: All angles are less than 90 degrees.

6. Obtuse triangle: One angle is greater than 90 degrees.

Based on Sides:

- Equilateral triangle: All three sides have equal length.
- Isosceles triangle: Two sides have equal length (base angles are also equal).
- Scalene triangle: All three sides have different lengths.

Based on Angles:

- Acute triangle: All three angles are less than 90 degrees.
- Right triangle: One angle is 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.

Based on Properties:

- Congruent triangles: All corresponding sides and angles are equal.
- Similar triangles: Corresponding angles are equal, but sides may be proportional in different sizes.
- Pythagorean theorem triangle: A right triangle with legs of length a and b and hypotenuse of length c, where a^2 + b^2 = c^2.

Special Cases:

- Equilateral right triangle: An equilateral triangle that is also a right triangle (all angles are 60 degrees).
- 30-60-90 triangle: An isosceles right triangle with angles of 30, 60, and 90 degrees.
- 45-45-90 triangle: An isosceles right triangle with angles of 45, 45, and 90 degrees.
- Golden triangle: A triangle with sides in the ratio of the golden ratio (approximately 1.618:1:1).