Library / UKMT Mathematical Olympiad for Girls /18 of 31

UKMT Mathematical Olympiad for Girls, 2016

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the trapezium $ABCD$ , the edges $AB$ and $DC$ are parallel. The point $M$ is the midpoint of $BC$ , and $N$ is the midpoint of $DA$ . Prove that $2MN = AB + CD$ .

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.