Question

In triangle $ABC$, $M$ is mid-point of $AB$ and a straight line through $M$ and parallel to $BC$ cuts $AC$ in $N$. Find the lenghts of $AN$ and $MN$ if $BC=7$ cm and $AC=5$ cm.

• A. $AN=2.5$ cm and $MN=3.5$ cm
• B. $AN=1.5$ cm and $MN=3.5$ cm
• C. $AN=2.5$ cm and $MN=4.5$ cm
• D. none of the above

Answer 1

Answer: (A)

$AN=2.5$ cm and $MN=3.5$ cm

M is the mid point of AB and MN II BC. Thus, N is the mid point of AC and

$MN=\frac{1}{2}BC$ (Mid point theorem)

$MN=\frac{1}{2}\left(7\right)$

$MN=3.5cm$
Also, $AN=\frac{1}{2}AC$

$AN=\frac{1}{2}\left(5\right)$

$AN=2.5cm$