Question

15. In equilateral triangle ABC, points D, E and F are midpoints of sides BC,
AC and AB. Which of the following statements are true?
​

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.

solution

Step-by-step explanation:

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Answer 2

Answer:

b. ∆ AFE is congruent to ∆ DEF

side AF = side DE ( Given )

side FE = side EF ( common side )

side AE = side DF ( Given )

angle A = angle D

angle E = angle F

angle F = angle E

these two triangle are equal as they are having their 6 properties equal.

why can't the other options be correct because -

a. ∆ ABC is bigger in size than ∆ DEF

c. ∆ BFD, it's angles like Angle B is not equal with angle D ( so as you know if all the 6 properties of two triangle is fully equal then only they are said to be congruent )

d. ( again the same thing as in option c )