Question

QUESTION:-IN ΔABC, D, E AND F ARE RESPECTIVELY THE MID POINTS OF SIDES AB, BC AND CA. SHOW THAT ΔABC IS DIVIDED INTO FOUR CONGRUENT TRIANGLES BY JOINING D,E AND F​

Answer 1

$\: \:$

Step-by-step explanation:

ABC is a triangle and D, E and F are mid-points of sides AB, BC and CA, respectively.

Then, AD = BD = 1/2AB

BE = EC = 1/2BC And

AF = CF = 1/2AC

Now, by mid-point theorem,

EF||AB and EF = 1/2AB = AD = BD

ED||AC and ED = 1/2AC = AF = CF

DF||BC and DF = 1/2BC = BE = CE

Now, in ΔADF and ∆EFD,

AD = EF

AF = DE

And DF = FD (common)

ΔADF ≅ ΔEFD

Similarly, ΔDEF ≅ ΔDEB

And ΔDEF ≅ ΔCEF

Thus, ΔABC is divided into four congruent triangles.