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Q.

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


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a

True

b

False 

answer is A.

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Detailed Solution

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