Chapter 4.6, Problem 33PPS

To determine

To show that the distance from B to F is three times the distance from D to F.

Explanation of Solution

Given information :

$\overline{BG}\cong \overline{HC},\overline{HD}\cong \overline{JF},\angle G\cong \angle H,\angle H\cong \angle J$

All the triangles are given isosceles.

Further it is given that $\overline{BG}\cong \overline{HC},\overline{HD}\cong \overline{JF},\angle G\cong \angle H,\angle H\cong \angle J$ .

From this information we get that,

$\begin{array}{l}\overline{BG}\cong \overline{HC}\\ \overline{GC}\cong \overline{HD}\end{array}$

Hence we can determine that triangle $\Delta BGC\cong \Delta CHD\cong \Delta DJF$

Therefore we can say that $\overline{BF}=\overline{BC}+\overline{CD}+\overline{DF}=3\overline{DF}$