Question

What is the missing step in the proof?

Statement: ∠GAC and ∠GAB are supplementary.
Reason: Linear Pair Theorem

Statement: ∠AFE≅∠AFD
Reason: Transitive Property of Equality

Statement: ∠GAC≅∠BAF
Reason: Vertical Angles Theorem

Statement: ∠GAC and ∠AFD are supplementary.
Reason: Linear Pair Theorem

Answer 1

the chart:
Given: BC¯¯¯¯¯ || DE¯¯¯¯¯, and ∠GAC≅∠AFD (figure).

Prove: GH←→⊥DE←→

Statement Reason
1. ∠GAC≅∠AFD given
2. ∠GAC≅∠AFE For parallel lines cut by a transversal, corresponding angles are congruent.
3.
4. ∠AFD and ∠AFE are
supplementary. Linear Pair Theorem
5. m∠AFD = m∠AFE = 90° If two congruent angles are supplementary, then each angle is a right angle.
6. GH←→⊥DE←→ definition of perpendicular lines