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Dear Student ,

Let ABC be an isosceles triangle where AB=ACNow, D, E and F are the mid points of sides AB, AC and BC respectively.In △ABC, By mid point theoremEF=12AB , DF=12AC, DE=12BCSince, AB=AC∴ 12AB=12AC ⇒EF = DF In △DEF, EF = DF.Hence, DEF is an isosceles triangle.


Regards

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Dear Student,
Consider ABC as an isosceles triangle, with AB = AC;
 (1/2)AB = (1/2)AC ----- (1)
If D is the midpoint of AB, then AD = (1/2)AB --------- (2)
Similarly if E is the midpoint of AC, then AE = (1/2)AC ------ (3)

Hence, from (1), (2) & (3), AD = AE

As two sides of the triangle ADE are equal, the triangle ADE is isosceles.

Regards

Hope it Helps :)
  • 1
Consider ABC as an isosceles triangle, with AB = AC;
 (1/2)AB = (1/2)AC ----- (1)
If D is the midpoint of AB, then AD = (1/2)AB --------- (2)
Similarly if E is the midpoint of AC, then AE = (1/2)AC ------ (3)

Hence, from (1), (2) & (3), AD = AE

As two sides of the triangle ADE are equal, the triangle ADE is isosceles.
  • 2
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