D, E and F are the mid points of side BC, CA and AB respectively of an equilateral triangle ABC. Show that DEF is also an equilateral triangle.
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prove DEF is an equilateral traingle
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given that
ABC is an equilateral triangle AB=BC=CAand D, E F are the midpoints of sides BC, CA and AB
therefore FE=1/2 of BC (midpoint theorem)-1
therefore FD=1/2 of AC (midpoint theorem) -2
therefore DE=1/2 of AB (midpoint theorem) -3
from 1,2,and3 we get
in triangle FE=FD=DE
therefore DEF is an equilateral triangle
ABC is an equilateral triangle AB=BC=CAand D, E F are the midpoints of sides BC, CA and AB
therefore FE=1/2 of BC (midpoint theorem)-1
therefore FD=1/2 of AC (midpoint theorem) -2
therefore DE=1/2 of AB (midpoint theorem) -3
from 1,2,and3 we get
in triangle FE=FD=DE
therefore DEF is an equilateral triangle
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