Theorem 10.1.5

Theorem: If three or more parallel lines makes congruent intercepts on the transversal, they also intercept congruent segments on any other line that cuts them.

Given: AB, CD and EF cut transversal GH at points P, Q and R respectively such that : $\overline{PQ}\cong\overline{QR}$
$\overleftrightarrow{XY}$ is another transversal cutting AB, CD, EF in points M,N,O respectively.

To Prove: $\overline{MN}\cong\overline{NO}$

Construction: Draw $\overline{MJ}$ and $\overline{NK}$ each parallel to GH meeting $\overline{CD}$ and $\overline{EF}$ respectively in points J and K.

Proof: