Question

If P and Q are the mid points of AB and CA respectively, then match the corresponding values of BC and PQ.

• A. PQ = 8 cm
• B. PQ = 7 cm
• C. BC = 8 cm
• D. BC = 18 cm

Answer 1

According to mid-point theorem,
"The line segment joining the midpoint of two sides of a triangle is said to be parallel to its third side and is also half of the length of the third side."
So, in the given figure, BC||PQ and $PQ=\frac{1}{2}BC$.

$\Rightarrow BC=2PQ$

Hence, the below table gives corresponding values of PQ and BC.

BC = 16 cm	$PQ=\frac{1}{2}\times 16=8cm$
BC = 14 cm	$PQ=\frac{1}{2}\times 14=7cm$
PQ = 4 cm	$BC=2\times 4=8cm$
PQ = 9 cm	$BC=2\times 9=18cm$