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ABC is an equilateral triangle. Points D, E, F are taken in sides AB, BC, CA respectively, so that AD = CF. Then AE, BF, CD enclosed a triangle which is :
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- equilateral triangle
- isosceles triangle
- right angle triangle
- None of these
- equilateral triangle
Correct Option: A
On the basis of given in question , we draw a figure of an equilateral triangle ABC ,
∵ AB = BC = AC
∴ AD = BE ⇒ BD = EC = CF = AF
∴ D, E and F are the mid points of AB, BC and CA respectively.
| DF || BC and DF = | BC | |
| 2 |
| EF || AB and EF = | AB | |
| 2 |
| DE || AC and DE = | AC | |
| 2 |
∴ DE = EF = FD
∴ ∆DEF is an equilateral triangle
