Question

Q.4:- In figure below, A ABC is equilateral triangle. Points D, E and F are midpoints of side AB, side AC and side BC respectively. Prove that A DEF is an equilateral triangle.​

Answer 1

answer

Let ABC be the triangle and D, E and F be the mid-point of BC, CA and AB respectively. We have to show triangle formed DEF is an equilateral triangle. We know the line segment joining the mid-points of two sides of a triangle is half of the third side.

Therefore DE=

2

1

AB,EF=

2

1

BC and FD=

2

1

AC

Now, ΔABC is an equilateral triangle

⇒AB=BC=CA

⇒

2

1

AB=

2

1

BC=

2

1

CA

⇒DE=EF=FD

∴ΔDEF is an equilateral triangle.

Answer 2

Answer:

Similarly ,E and F are the mid - points of AC and AB respectively . F and D are the mid - points of AB and BC respectively . Now, △ABC is an equilateral triangle . Hence, ∆FED is an equilateral triangle

Step-by-step explanation:

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