The triangle transitive congruent is proved by considering that if one triangle is congruent to second triangle and second triangle is congruent to third one, then the first triangle is congruent to third triangle.
Transitive Property of Congruence :
The transitive property states that if one geometry is congruent with another, and the second is congruent with a third, then the first is also congruent with the third.
Statement : If triangle ABC is similar to triangle PQR and triangle PQR is similar to triangle EFG , then triangle ABC is similar to triangle EFG.
Given, ∆ABC ≅ ∆PQR and ∆PQR ≅ ∆EFG
RTP -> ∆ABC ≅ ∆EFG.
Proof : ∆ABC ≅ ∆PQR, SSA Congruence which implies, AB = PQ --(1)
PR = AC --(2)
and angle ABC = angle PQR --(3)
∆PQR ≅ ∆EFG, AAS Congruence which gives
Angle PQR = Angle EFG --(4)
PQ = EF --(5)
Angle PRQ = Angle EGF --(6)
from (3) and (4) we get,
angle ABC = Angle EFG --(7)
from (1) and (5) we get , AB = EF --(8)
angle BAC = angle FEG = 40° --(9)
Now, from (7) , (8), (9) we conclude that the triangle ABC is Congruent to triangle EFG by ASA Congrauance postulate i.e ∆ABC ≅ ∆EFG.
Hence proved.
To learn more about Transitive property in Congruence, refer:
https://brainly.com/question/29792714
#SPJ4
