Question

In the given figure, D and E are mid points of sides AB and AC of $△$ABC. Which of the following is true ?

• A. $DE=\frac{1}{2}BC$, by mid point theorem
• B. ​$DE=\frac{1}{2}BC$ , by converse of mid point theorem
• C. $DE=\frac{1}{2}AB$, by mid point theorem
• D. $DE=\frac{1}{2}AB$, by converse of mid point theorem

Answer 1

The correct option is A

$DE=\frac{1}{2}BC$, by mid point theorem

Mid point theorem states that a line joining the mid points of 2 sides of a triangle is parallel to the third side and is half of it.

Therefore, by mid point theorem, $DE=\frac{1}{2}BC$ and DE ||BC.