Question

ABCD is a quadrilateral in which AB || DC and AD || BC. A line MN, parallel to CD, is drawn meets the midpoint M of the side BC which meets AD at N. What can you say about the diagonal AC?

• A. None of the above.
• B. Line MN bisects AC.
• C. Line AC is twice the length AD.
• D. Line AC is $\frac{1}{3}$rd the length MN.

Answer 1

The correct option is B Line MN bisects AC.


Since AB, CD and MN are all parallel lines, we can think of AD, AC and BC as transversals on the parallel lines.
$\therefore$ By equal intercept theorem, AN = ND and AO = OC.
$\Rightarrow$ Line MN bisects diagonal AC.