A triangle is a polygon with three sides and three angles. There are several important attributes and properties to understand:

### 1. **Sides:**
   - A triangle has three sides, typically labeled as \( a \), \( b \), and \( c \). The sum of the lengths of any two sides must always be greater than the length of the remaining side (Triangle Inequality Theorem).

### 2. **Angles:**
   - The sum of the three interior angles of a triangle is always **180 degrees**. Depending on the angles, triangles can be classified as:
     - **Acute**: All angles are less than 90°.
     - **Right**: One angle is exactly 90°.
     - **Obtuse**: One angle is greater than 90°.

### 3. **Types of Triangles (by sides):**
   - **Equilateral Triangle**: All three sides are equal, and each angle is 60°.
   - **Isosceles Triangle**: Two sides are equal, and the angles opposite these sides are also equal.
   - **Scalene Triangle**: All three sides are of different lengths, and all angles are different.

### 4. **Perimeter and Area:**
   - **Perimeter**: The perimeter \( P \) of a triangle is the sum of the lengths of its three sides:
     \[
     P = a + b + c
     \]
   - **Area**: The area \( A \) of a triangle can be calculated using various formulas, including:
     - **Base-Height Formula**: \( A = \frac{1}{2} \times \text{base} \times \text{height} \)
     - **Heron's Formula**: For sides \( a \), \( b \), and \( c \), with the semi-perimeter \( s = \frac{a + b + c}{2} \):
       \[
       A = \sqrt{s(s - a)(s - b)(s - c)}
       \]

### 5. **Special Points:**
   - **Centroid**: The point where the three medians of the triangle intersect. It is the triangle's center of mass.
   - **Incenter**: The point where the angle bisectors intersect, equidistant from all sides.
   - **Circumcenter**: The point where the perpendicular bisectors of the sides meet, equidistant from all vertices. It is the center of the circumcircle (the circle that passes through all vertices).
   - **Orthocenter**: The point where the three altitudes (heights) meet.

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Would you like more details on any of these? Or have any specific questions?

### Related Questions:
1. What is Heron's formula and when is it useful?
2. How do you find the centroid of a triangle?
3. What is the difference between a circumcenter and an incenter?
4. How can you determine if a triangle is right-angled from its sides?
5. How is the Pythagorean Theorem used in triangles?

**Tip**: Always verify that the sum of two sides of a triangle is greater than the third side before proceeding with calculations (Triangle Inequality Theorem).

Learn the key attributes of triangles, including their sides, angles, types, and important formulas like perimeter, area, and Heron's formula. Understand key geometric concepts such as the Triangle Inequality Theorem and the Sum of Interior Angles Theorem. Perfect for students in Grades 6-9.

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