Question

what is the missing step in the proof? given: $overline{bc}paralleloverline{de}$, and $angle gaccongangle afd$ (figure). prove: $overleftrightarrow{gh}perpoverleftrightarrow{de}$ statement: $angle gac$ and $angle gab$ are supplementary. reason: linear pair theorem statement: $angle afecongangle afd$ reason: transitive property of equality statement: $angle gaccongangle baf$ reason: vertical angles theorem statement: $angle gac$ and $angle afd$ are supplementary. reason: linear pair theorem

statement	reason
2. $angle gaccongangle afe$	for parallel lines cut by a transversal, corresponding angles are congruent.
3.
4. $angle afd$ and $angle afe$ are supplementary.	linear pair theorem
5. $mangle afd = mangle afe=90^{circ}$	if two congruent angles are supplementary, then each angle is a right - angle.
6. $overleftrightarrow{gh}perpoverleftrightarrow{de}$	definition of perpendicular lines

Explanation:

Step1: Analyze given and previous steps

We know $\angle GAC\cong\angle AFD$ (given) and $\angle GAC\cong\angle AFE$ (corresponding - angles for parallel lines). Also, we know $\angle AFD$ and $\angle AFE$ are supplementary from the linear - pair theorem later.

Step2: Determine the missing step

The missing step should be $\angle AFE\cong\angle AFD$ by the transitive property of equality since $\angle GAC\cong\angle AFD$ and $\angle GAC\cong\angle AFE$.

Answer:

Statement: $\angle AFE\cong\angle AFD$
Reason: Transitive Property of Equality