Question

if one of the pair of alternate angles is congruent the the lines arem​

Answer 1

Question ⤵️

if one of the pair of alternate angles is congruent the the lines aarem.

Answer ⤵️

Proposition 1.27 of Euclid's Elements, a theorem of absolute geometry (hence valid in both hyperbolic and Euclidean Geometry), proves that if the angles of a pair of alternate angles of a transversal are congruent then the two lines are parallel (non-intersecting).

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Answer 2

Answer:

If one pair of alternate angles is congruent then the lines are parallel