Identify the triangle by its sides and angles.

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1. **Classifying by Sides**

- If all three sides are equal, i.e., $$a = b = c$$, then the triangle is **equilateral**.
   - If exactly two sides are equal, for instance $$a = b \neq c$$, then the triangle is **isosceles**.
   - If no sides are equal, i.e., $$a \neq b \neq c$$, then the triangle is **scalene**.

2. **Classifying by Angles**

- Use the fact that the sum of the interior angles is $$180^\circ$$:
     $$
     A + B + C = 180^\circ
     $$
   - If one of the angles is exactly $$90^\circ$$ (for example, $$A = 90^\circ$$), then the triangle is a **right triangle**.
   - If one of the angles is greater than $$90^\circ$$ (say, $$A > 90^\circ$$), then the triangle is **obtuse**.
   - If all angles are less than $$90^\circ$$, then the triangle is **acute**.

3. **Example**

Suppose a triangle has sides $$a$$, $$b$$, and $$c$$ and angles $$A$$, $$B$$, and $$C$$:
   
   - If $$a = b = c$$, then automatically, the triangle is equilateral and each angle is:
     $$
     A = B = C = \frac{180^\circ}{3} = 60^\circ
     $$
     Thus, it is also acute.
   
   - If $$a = b \neq c$$ and one of the angles is $$90^\circ$$, then the triangle is both isosceles and right.
   
   - If $$a$$, $$b$$, and $$c$$ are all different, and one of the angles exceeds $$90^\circ$$, say $$A > 90^\circ$$, then the triangle is scalene and obtuse.

By comparing the side lengths and measuring the angles, you can identify the classification of the triangle based on the above criteria.
A triangle can be classified based on its sides and angles as follows: - **By Sides:** - **Equilateral:** All three sides are equal. - **Isosceles:** Exactly two sides are equal. - **Scalene:** All sides are of different lengths. - **By Angles:** - **Right Triangle:** One angle is exactly 90 degrees. - **Obtuse Triangle:** One angle is greater than 90 degrees. - **Acute Triangle:** All angles are less than 90 degrees. By measuring the sides and angles of a triangle, you can determine its classification as equilateral, isosceles, scalene, right, obtuse, or acute.

Identify the triangle by its sides and angles.

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