Question

In the given figure, if $PQ : BC = 1 : 3$, then the ratio of $AP : PB$ will be:

• A. $1 : 4$
• B. $1 : 3$
• C. $1 : 2$
• D. $2 : 3$

Hint:

In similar triangles, the line parallel to one side divides the other two sides in the same ratio.

Answer 1

The Correct Option is D

Step 1: Apply Basic Proportionality Theorem (Thales' Theorem).
According to the Basic Proportionality Theorem, if a line parallel to one side of a triangle intersects the other two sides, then the two sides are divided proportionally.
In the given figure, $PQ \parallel BC$, so according to the theorem: \[ \frac{AP}{PB} = \frac{AQ}{QC} \]
Step 2: Use the given ratio.
We are given that $PQ : BC = 1 : 3$. Hence, the ratio of $AQ$ to $QC$ is also $1 : 3$.
Thus, we have: \[ \frac{AP}{PB} = \frac{1}{3} \]
Step 3: Conclusion.
Therefore, the ratio of $AP : PB$ is $2 : 3$.