Question
Sun September 13, 2009 By:

MID PTS THEOREM

Expert Reply
Sun September 13, 2009

ΔABC is equilateral triangle, A = B = C = 60

and AB = BC = AC,

AD = DB.

AD + DB = AB

2 AD = AB

AD = AB/2

Similarly AF = AC/2

AF = AD since AC = AB.............(2)

ΔADF,

  A = 60 and  AFD = ADF .....from (2)

Hence AFD = ADF = 60.

Similary in,

ΔBDE,

BD = BE

  B = 60 and  BDE = DEB .....from (2)

Hence BDE = DEB = 60.

BDE + ADF + FDE = 180.

 FDE = 60.

Similarly in ΔDEF, the remaining two angles can be shown to be 60.

Hence triangle DEF is an equilateral triangle.

Regard,

Team,

TopperLearning.

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