Question

Q) Prove that the medians of an equilateral triangle are equal.
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Answer 1

Step-by-step explanation:

Let ΔABC be an equilateral triangle with AD,BE and CF as its medians.

Let AB=AC=BC=x units

In triangles BFC and CEB, we have

BF=CE [∵AB=AC⇒

2

1

AB=

2

1

AC⇒BF=CE]

∠ABC=∠ACB [Each equal to 60

∘

]

and, BC=BC [Common]

So by SAS congruence criterion, we obtain

ΔBFC≅ΔCEB⇒BE=CF

Similarly, we have AB=BE

Hence, AD=BE=CF