Chapter 9.1, Problem 63SR

To determine

To find: The inequality for $\mathrm{m}\angle \mathrm{F}\mathrm{B}\mathrm{A}$ and $\mathrm{m}\angle \mathrm{D}\mathrm{B}\mathrm{F}$ .

Answer to Problem 63SR

The inequality for $\mathrm{m}\angle \mathrm{F}\mathrm{B}\mathrm{A}$ and $\mathrm{m}\angle \mathrm{D}\mathrm{B}\mathrm{F}$ is $\mathrm{m}\angle \mathrm{D}\mathrm{B}\mathrm{A}>\mathrm{m}\angle \mathrm{D}\mathrm{B}\mathrm{F}$ .

Explanation of Solution

Given information: The figure is shown below.

  

Calculation:

Since, in triangle FBA and DBF $\overline{\mathrm{B}\mathrm{F}}\cong \overline{\mathrm{F}\mathrm{B}},\overline{\mathrm{A}\mathrm{B}}\cong \overline{\mathrm{B}\mathrm{D}}$ and $\mathrm{A}\mathrm{F}>\mathrm{D}\mathrm{F}$ .

Thus, by converse of the hinge theorem $\mathrm{m}\angle \mathrm{D}\mathrm{B}\mathrm{A}>\mathrm{m}\angle \mathrm{D}\mathrm{B}\mathrm{F}$