幾何實驗室

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Following the above constructions, we can develop the angle bisector under the upper half-plane model.

Given:

Three points A, B and C in the upper half-plane.

To Construct:

The u-line which bisects the angle determined by B-A-C with vertex A in non-Euclidean sense.

Constructions:

Figure 26

Continue the above constructions; let straight-line r be the angle bisector of angle in Euclidean sense (see Figure 26).
Construct the line through A, which is perpendicular to r and intersects the x-axis at R.
Then the u-line through A and with Euclidean center R satisfies the desired conditions.

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