Question

Draw an equilateral triangle and any one median. Prove that the 2 triangles formed by the median are
congruent using any one criterion. Justify your answer with necessary properties.

Answer 1

Answer:

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