Answer :
1. angle BFG is congruent to angle BDE : given
2. Line BF bisect angle AFD : given
3. angle GAF is congruent to EDF : given
4. angle AFG is congruent to angle DFE : corresponding angles
5. Triangle GAF is similar to triangle EDF : AA similarity postulate.
Similar triangles are triangles with equal Corresponding angles and equal side ratio. This means that their side length differs but in proportion.
To prove that
Triangle GAF is similar to triangle EDF
1. angle BFG is congruent to angle BDE : given
2. Line BF bisect angle AFD : given
3. angle GAF is congruent to EDF : given
4. angle AFG is congruent to angle DFE : corresponding angles
Since the angles of the triangles are equal and their side length differ , we can say that
5. Triangle GAF is similar to triangle EDF : AA similarity postulate.
