Is it true that the medians of an equilateral triangle are equal?

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True

False

answer is A.

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Detailed Solution

Given that the medians of an equilateral triangle are equal.
Question Image

△ ADC

and

△ BEA

,
AB = AC (Since

△ ABC

is an equilateral triangle)
∠DCA = ∠BCE (Common angle)
∠ADC = ∠BEA = 90°
So,

△ ADC ⩭ △ BEA

. [By ASA congruence rule].
Then, AD = BE since the two triangles are congruent.
Similarly, BE = CF.
Hence, AD = BE = CF.
Hence, the medians of the equilateral triangle are equal.
So, the given statement is true and the correct option is 1.

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