Work the following problem in absolute geometry: If lines ℓ and m are cut by a transversal...

Work the following problem in absolute geometry: If lines ℓ and m are cut by a transversal so that a pair of alternate interior angles are congruent, then ℓ and m have a common perpendicular. Do not use any of the results of this section that depend on the Euclidean Parallel Postulate. (Hint: In the accompanying figure, the angles at A and B are congruent, as indicated. Drop perpendiculars from the midpoint M to ℓ and m at C and D.