Question

proof in exercises 13 and 14, write a two - column proof. (see example 4.) 13. given ∠gfh≅∠ghf prove ∠efg and ∠ghf are supplementary. 14. given (overline{ab}congoverline{fg}), (overline{bf}) bisects (overline{ac}) and (overline{dg}). prove (overline{bc}congoverline{df})

Explanation:

Step1: Recall linear - pair property

$\angle EFG+\angle GFH = 180^{\circ}$ (linear - pair of angles are supplementary)

Step2: Use the given equality

Since $\angle GFH\cong\angle GHF$, we can substitute $\angle GFH$ with $\angle GHF$ in the above equation.
So, $\angle EFG+\angle GHF = 180^{\circ}$

Answer:

$\angle EFG$ and $\angle GHF$ are supplementary.