Question

In triangle ABC ; M is mid-point of AB, N mid-point of AC and D is any point in base BC. Then:

• A. MN bisects AD
• B. MN divides AD in the ratio 1:3
• C. MN divides AD in the ratio 1:2
• D. MN divides AD in the ratio 1:4

Answer 1

The correct option is A MN bisects AD

In $△ABC$, $M$ is mid point of $AB$ and $N$ is mid point of $AC$
$D$ is any point of BC
Now, Join AD and MN such that they met at O
In $△ABC$
M is mid point of AB and N is mid point point of AC
Hence, $MN\parallel BC$ and $MN=\frac{1}{2}BC$
Now, In $△ABD$
$MO\parallel BC$ and M is mid point of AB
Thus, $O$ is mid point of AD
Hence, $MN$ bisects $AD$