Prove theorem 2.6.4.  If P is any point, then there are at least two distict lines l and m such that P lies on both l and

Let l1,l2, l3 be three parallel lines and let t, and t2 be traversals intersecting these lines. Let i = 1,2,3. t1 A¡ = t1 N li, Bị = t2 N lị , A, A2 Prove the segments created are proportional. That is, A3 A1 A2 prove B1B2 B2B3 t2 A2A3 B2 B3 B1

5. Determine whether the following pair of lines is parallel, intersects at a single point, or is skew. If the lines are parallel, determine whether they are the same line (and thus intersect at all points). If the lines intersect at a single point, determine the point of intersection: r(t) = (0, 1, 2) + t(1, 1, 1), R(s) = (-2, 1,0) + s(-1, -3, -1).

Show that Congruence Axiom 1 fails. (Hint. Consider the line segment from A = (0, 0) to B = (1, 1). ‹enconsider the points P = (1, 0) and Q = (2, 0). Use the distance formulaD((x1, y1), (x2, y2)) = √(x1 − x2)2 + (y1 − y2)2to show that there is no point R on −−→P Q so that AB ∼= P R.)