Question

If the line \(PQ\) is parallel to line \(BC\) of \(\triangle ABC\), then

• A. \(\frac{AP}{PB} = \frac{AQ}{QC}\)
• B. \(\frac{AB}{AC} = \frac{AP}{AQ}\)
• C. \(\frac{AP}{AQ} = \frac{AB}{AC}\)
• D. \(\frac{BC}{AC} = \frac{AB}{AQ}\)

Hint:

Use Thales's theorem to solve problems involving parallel lines and triangles.

Answer 1

The Correct Option is A

By the basic proportionality theorem (Thales's theorem), when a line is parallel to one side of a triangle, it divides the other two sides in the same ratio. Thus, \(\frac{AP}{PB} = \frac{AQ}{QC}\). Thus, the correct answer is \(\frac{AP}{PB} = \frac{AQ}{QC}\).