Calculator
The result appears above this form after submission.
Plotly Graph
This graph compares theorem values visually.
Formula Used
The triangle midsegment theorem states that a segment joining the midpoints of two sides is parallel to the third side. Its length is always half the third side. The smaller triangle created is similar to the original triangle.
How to Use This Calculator
- Select the calculation mode.
- Enter the known length values.
- Add a tolerance if you want a verification check.
- Choose a unit label for clearer results.
- Set segment names if you want a custom parallel statement.
- Click Calculate Now.
- Review the result card, graph, and theorem metrics.
- Export the final output as CSV or PDF.
Example Data Table
| Mode | Third Side | Midsegment | Ratio | Note |
|---|---|---|---|---|
| Find midsegment | 18 | 9 | 1:2 | 9 is half of 18 |
| Find midsegment | 26 | 13 | 1:2 | Works for any valid triangle |
| Find third side | 32 | 16 | 1:2 | Third side doubles midsegment |
| Verify relation | 21 | 10.5 | 1:2 | Verified exactly |
| Verify relation | 15 | 7.49 | ≈1:2 | Close under small tolerance |
FAQs
1. What does the triangle midsegment theorem say?
A segment joining two side midpoints is parallel to the third side. Its length is exactly half that third side.
2. Can this calculator solve both directions?
Yes. It finds the midsegment from a known third side, or finds the third side from a known midsegment.
3. What does the verify mode do?
Verify mode checks whether your entered lengths satisfy the half-length rule. It also shows the difference and the expected value.
4. Why is tolerance included?
Tolerance helps when values are rounded. Small measurement errors can still pass verification if the difference stays within your allowed margin.
5. Does the theorem depend on triangle type?
No. The relationship works for any triangle, including acute, right, and obtuse triangles, as long as the segment joins true midpoints.
6. What ratio should I expect?
The midsegment-to-third-side ratio is always 1:2. In decimal form, the ratio is 0.5 or 50%.
7. Can I export the results?
Yes. When a result exists, the page provides CSV and PDF export buttons for fast saving and sharing.
8. What units should I use?
Use any consistent unit, such as centimeters, meters, inches, or feet. The theorem works the same across all units.