We work in hyperbolic geomtery We have a AAec as un beow on

We work in hyperbolic geomtery:

We have a AAec as un beow on is a point P nad (nas nesses trungn does not inter est

Solution

We call a neutral geometry satisfying the Euclidean Parallel Property a Euclidean geometry. We call a neutral geometry satisfying the Hyperbolic Parallel Property a hyperbolic geometry

Here AP is a line, D AP, and B and C two points such that C B D, QD QD = s, and P D = t. Let C and E be points on the same side of P D with m(DP C) = (t) and m(DQE) = (t). Then P C is parallel to ` and P C is parallel to QE (since QD is a transversal of P C and QE with a pair of congruent corresponding angles, and hence congruent alternating interior angles). Since Q and D are on opposite sides of P C, it follows that QE ` = . In particular, QE ` = , so (s) m(DQE) = (t).