In Fig. 5.30, AM and DN are the medians. Then find the value of DF.

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There are many ways to prove that the 2 triangls are equal.

​​We know that median that it bisects a line into 2 equal halves.
BM = MC ____1
​EN =  NF ____2
BM = EN ____3
​from 1, 2 and 3
MC = NF

​Prove the congreunecy of triangles ABM and DEN by SSS congreuency.
​from these 2 congruent triangles we have proved now,
​take angle A & D and B & E
​angle AMC = DNF (the exterior angle is equal to both interior and opposite angles) (adding equals to equals the sums are equals A + B = D + E)
​by SAS congreuency prove triangles AMC and DNF are congruent
AM = DN
M = N
​MC = NF
so by cpct
​AC = DF
​AC = 6 cm
​So DF = 6 cm (proved)
​
 

DF=6cm

Reason:

In triangles ABM and DEN,
AB = DE
BM = EN
AM = DN
​Therefore, ABC congruent DEF