theorem Th21: :: EUCLID_6:21

for p1, p2, p3, p4, p5, p6 being Point of (TOP-REAL 2) st p1,p2,p3 is_a_triangle & p4,p5,p6 is_a_triangle & angle (p1,p2,p3) = angle (p4,p5,p6) & angle (p3,p1,p2) = angle (p6,p4,p5) holds
( |.(p3 - p2).| * |.(p4 - p6).| = |.(p1 - p3).| * |.(p6 - p5).| & |.(p3 - p2).| * |.(p5 - p4).| = |.(p2 - p1).| * |.(p6 - p5).| & |.(p1 - p3).| * |.(p5 - p4).| = |.(p2 - p1).| * |.(p4 - p6).| )