Prove that the two triangles are congruent using the SAS congruence criteria. Show your work.
Triangle DEF: D(3,2), E(5,3), F(4,5)
Triangle FGH: F(4,5), G(3,7), H(5,8)
Given: ∠DFE and ∠GFH are vertical angles
To prove that the two triangles are congruent using the SAS congruence criteria, we need to show that they have two congruent sides and the angle between those sides is congruent.
1. Side DF is congruent to side FG because they have the same length and share point F.
2. Side FE is congruent to side GH because they have the same length and share point G.
3. ∠DFE is congruent to ∠GFH because they are vertical angles and therefore congruent.
Therefore, by the SAS congruence criteria, Triangle DEF and Triangle FGH are congruent.