(a) Is the converse of this theorem true or false? Let A1, B1 and C1 be points on line m1 and let A2, B2 and C2 be points on line m2. If the lines A1A2, B1B2, C1C2 are parallel, then the ratios (A1B1/B1C1) and (A2B2/B2C2) are equal.

(b) If m1 is parallel to m2, with points A1, B1 and C1 on m1 and A2, B2 and C2 on m2, if (A1B1/B1C1) = (A2B2/B2C2) then the lines A1A2, B1B2, C1 C2 are either concurrent or parallel.

Hint: See B&B Problem 4, page 127. This problem is phrased more simply: If three lines cut off proportional segments on two parallel lines, then the three lines are either concurrent or parallel.