Chapter 7.4, Problem 28PPS

To determine

To write: The paragraph proof of Corollary $7.1$ .

Explanation of Solution

Given information:

The given Corollary is, “If three or more parallel lines intersect two transversals, then they cut off the transversals proportionality”.

The given Corollary is, “If three or more parallel lines intersect two transversals, then they cut off the transversals proportionality”.

Consider the following figure,

  

From the above statement, $\overline{AD}\left|\right|\overline{BE}\left|\right|\overline{CF}$ .

In $\Delta GBE,\overline{AD}\left|\right|\overline{BE}$ :

From the proportionality theorem,

  $\frac{AB}{DE}=\text{Constant}$

In $\Delta GCF,\overline{BE}\left|\right|\overline{CF}$ :

From the proportionality theorem,

  $\frac{BC}{EF}=\text{Constant}$

From the above equations,

  $\begin{array}{l}\frac{AB}{DE}=\frac{BC}{EF}\\ \frac{AB}{BC}=\frac{DE}{EF}\end{array}$

Hence, if three or more parallel lines intersect two transversals, then they cut off the transversal proportionality.