28 October 2021

This entry is just an addendum to yesterday's communication. Now several new examples work correctly, and there is also support for proving inequalities directly.

Please follow these steps to directly prove the triangle inequality:

1. Click on the 5. toolset in the Toolbar and select the first tool (Polygon ).
2. Draw a triangle in the Graphics area (on the right) by creating three points, and then click on the first point again.
3. Click on the last, empty line in the Algebra view (on the left) and type Prove(a+b>c) and press ENTER.
4. GeoGebra reports true as the result of the computation.

At the moment, you can safely try the following examples:

• Prove that \(a^2+b^2>\frac{c^2}2\) in an arbitrary triangle. You may need to play a bit with the formula editor to enter the command correctly.
• Disprove that \(a^2+b^2\leq\frac{c^2}2\) in an arbitrary triangle.
• Prove that \(a^2+b^2>\frac{c^2}3\) in an arbitrary triangle.
• Disprove that \(a^2+b^2>0.51c^2\) in an arbitrary triangle.

And a lot of additional ones... Good luck!