MID PTS THEOREM
Asked by | 13th Sep, 2009, 06:41: AM
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)
A = 60 and AFD = ADF .....from (2)
Hence AFD = ADF = 60.
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.
Answered by | 13th Sep, 2009, 02:44: PM
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