Chapter 1, Problem 14RP

To determine

To Prove: The given statement $\angle EDF\cong \angle FDG\cong \angle GDH$ has to be concluded with reference to the information provided

Explanation of Solution

Given information: The following information has been given

  $\overrightarrow{DF}$ and $\overrightarrow{DG}$ trisect $\angle EDH$

Formula used: Any angle trisectors will divide the trisected angle into three equal parts

Proof: Using the information that $\overrightarrow{DF}$ and $\overrightarrow{DG}$ trisect $\angle EDH$ , we can say that $\overrightarrow{DF}$ and $\overrightarrow{DG}$ being the angle trisectors, they trisect the $\angle EDH$ into three equal parts.

Hence, if the three angles are equal, we can say that they are congruent as well.

Thus,

  $\angle EDF\cong \angle FDG\cong \angle GDH$

Hence, the given statement has been proved