Question

What is BC ?

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Answer 1

Answer: BC= 8 units.

Explanation:

In the given figure m, we have a Δ ABC in which point D and F are the mid point of sides AB and AC respectively .

We know that the Mid - segment theorem says that a line segment that connects the midpoints of two sides of a triangle is parallel to the third side and it should be equal to one-half of the third side.

Therefore , For the given situation , we have

`DF=(1)/(2)BC\\\\\Rightarrow\ BC= 2 DF`

Since DF = 4 units [Given ]

Then,
`BC= 2(4)= 8\text{ units}`

Hence, BC= 8 units.

Answer 2

The length of BC is 8 units.

Solution-

Mid-Point Theorem-

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

As given,

AD = DB, so D is the mid point of AB

FA = FC, so F is the mid point of AC

Hence, DF is the line segment connecting the midpoints of two sides of a triangle.

Applying the theorem,

BC = 2DF = 2×4 = 8 units