1. What are Similar Triangles?

Similar triangles are triangles that have the same shape but not necessarily the same size. They have equal corresponding angles and proportional corresponding sides.

2. How Does the Calculator Work?

The calculator uses the properties of similar triangles:

Where:

• \( side_1, side_2 \) — Sides of the first triangle
• \( corresponding_1, corresponding_2 \) — Corresponding sides of the second triangle
• \( ratio \) — Proportionality constant between the triangles

Explanation: The calculator finds the ratio between known corresponding sides, then uses this ratio to find unknown sides.

3. Importance of Similar Triangles

Details: Similar triangles are fundamental in geometry and have practical applications in surveying, architecture, and engineering for indirect measurement.

4. Using the Calculator

Tips: Enter any three values (two corresponding sides and one other side) to find the ratio and the corresponding side. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What proves triangles are similar?
A: Triangles are similar if their corresponding angles are equal (AA), or their sides are proportional (SSS), or two sides are proportional and included angles equal (SAS).

Q2: Can I use this for right triangles?
A: Yes, right triangles can be similar if their corresponding angles are equal (including the right angle).

Q3: What units should I use?
A: The calculator works with any consistent units (meters, feet, etc.), but all inputs must be in the same units.

Q4: How accurate are the results?
A: Results are mathematically exact based on the inputs. Rounding is done only for display purposes.

Q5: Can I find angles with this calculator?
A: No, this calculator only works with side lengths. Angle measures must be known or determined separately.