Question

In the given triangle, the lines MN, PQ and BC are parallel to each other and AM = MP = PB. Which of the following statements is/are true?

• A. $MN=\frac{1}{2}BC$
• B. AN=NQ
• C. AN = QC
• D. $MN=\frac{1}{4}BC$

Answer 1

Answer: (B), (C)

The correct options are
B

AN=NQ

C

AN = QC

Consider the parallel lines MN, PQ and BC and think of AB and AC as transversals.
$\therefore$ Since AB cuts equal intercepts on the three parallel lines, by "Equal Intercept theorem",the intercepts cut by AC will also be equal.
$\therefore$ AN = NQ = QC.
Hence, the correct answer options are (b),(c),(d).