Classify Triangle By Sides Calculator

Triangle Classification Rules:

\[ \text{type} = \begin{cases} \text{equilateral} & \text{if } a = b = c \\ \text{isosceles} & \text{if } a = b \text{ or } b = c \text{ or } a = c \\ \text{scalene} & \text{otherwise} \end{cases} \]

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1. What is Triangle Classification?

Triangle classification by sides is a method to categorize triangles based on the lengths of their sides. The three main types are equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides different).

2. How Does the Calculator Work?

The calculator uses the following classification rules:

\[ \text{type} = \begin{cases} \text{equilateral} & \text{if } a = b = c \\ \text{isosceles} & \text{if } a = b \text{ or } b = c \text{ or } a = c \\ \text{scalene} & \text{otherwise} \end{cases} \]

Where:

\( a \) — Length of side a
\( b \) — Length of side b
\( c \) — Length of side c

Explanation: The calculator first verifies the input values can form a valid triangle (sum of any two sides must be greater than the third), then classifies the triangle based on side length equality.

3. Importance of Triangle Classification

Details: Classifying triangles helps in understanding their properties and solving geometric problems. Different triangle types have different properties regarding angles, symmetry, and area calculations.

4. Using the Calculator

Tips: Enter positive values for all three sides. The calculator will first check if the sides can form a valid triangle before classification. All values must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What makes a valid triangle?
A: For three lengths to form a triangle, the sum of any two sides must be greater than the third side (Triangle Inequality Theorem).

Q2: Can a triangle be both isosceles and right?
A: Yes, a right triangle with two equal sides (and angles) is called an isosceles right triangle.

Q3: What's special about equilateral triangles?
A: All angles are 60°, they have three lines of symmetry, and all medians/altitudes/angle bisectors coincide.

Q4: How precise are the calculations?
A: The calculator checks for exact equality (to 4 decimal places). Very small differences will classify as scalene.

Q5: Can decimals be used?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.