Chapter 4.6, Problem 10WE

To determine

Prove $\angle B\cong \angle F$

Explanation of Solution

Given:

Congruent parts are marked in the figure.

Calculation:

The diagram is :

Draw auxiliary lines AE and AC .

  

Consider the $\Delta ACD\text{ and }\Delta AED$ :

  $\overline{CD}\cong \overline{ED}$

  $\angle CDA\cong \angle DEA$

  $\overline{AD}\cong \overline{AD}$

So, by SAS Postulate , $\Delta ACD\cong \Delta AED$ .

Hence , $\overline{AC}\cong \overline{AE}$

Consider the $\Delta ABC\text{ and }\Delta AFE$ :

  $\overline{AB}\cong \overline{AF}$

  $\overline{BC}\cong \overline{FE}$

  $\overline{AC}\cong \overline{AE}$

So, by SSS Postulate , $\Delta ABC\cong \Delta AFE$

Hence , $\angle B\cong \angle F$

Hence proved.