1. What is the Triangle Proportionality Theorem?

The Triangle Proportionality Theorem states that if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

2. How Does the Calculator Work?

The calculator uses the Triangle Proportionality Theorem formula:

Where:

• \( side1 \) — Length of the first side
• \( side2 \) — Length of the second side
• \( segment\_corresponding \) — Length of the corresponding segment

Explanation: The theorem shows the proportional relationship between corresponding parts of divided triangle sides.

3. Importance of the Theorem

Details: This theorem is fundamental in geometry for solving problems involving similar triangles and proportional relationships in geometric figures.

4. Using the Calculator

Tips: Enter the lengths of the two sides and the corresponding segment. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between this and the Basic Proportionality Theorem?
A: They are essentially the same theorem, just known by different names in different regions.

Q2: Does this work for all triangles?
A: Yes, as long as the line is parallel to one side and intersects the other two sides.

Q3: Can this be used for right triangles?
A: Absolutely, the theorem applies to all types of triangles including right triangles.

Q4: What units should I use?
A: Any consistent units can be used (cm, m, inches, etc.) as long as all measurements are in the same units.

Q5: How accurate are the results?
A: The results are mathematically exact based on the theorem, assuming precise input values.