Prove that the medians of an equilateral triangle are equal.
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let all sides be 'a'units.
draw a triangle ABC and draw a median from A to Side BC.
as we know that the median of an equilateral triangle is also the altitude of the triangle.
So the median AD is also altitude.
So BD is a/2 and DC is also a/2.
in triangle ABD, BD^2=AC^2 - BD^2
BD^2= a^2 - (a/2)^2
=4a^2/2 - a^2/4
= 3a^2/4
BD= √(3a^2/4)
= √3/2 a
SIMILARLY ON ALL SIDES DO THE SAME METHOD
draw a triangle ABC and draw a median from A to Side BC.
as we know that the median of an equilateral triangle is also the altitude of the triangle.
So the median AD is also altitude.
So BD is a/2 and DC is also a/2.
in triangle ABD, BD^2=AC^2 - BD^2
BD^2= a^2 - (a/2)^2
=4a^2/2 - a^2/4
= 3a^2/4
BD= √(3a^2/4)
= √3/2 a
SIMILARLY ON ALL SIDES DO THE SAME METHOD
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