Hi all, first of all - my first post here. Nice to meet you all. I'm active on mymathforum if you guys post there from time to time. My name is Oria, I live in israel, I'm a math private teacher for pre uni students, and I study applied mathematics in holon institute of technology.

Anyway here's my question. A student of mine asked me to solve it and I was stumped, was actually quite embarrasing since it is so simple.

23.png picture by oriagr - Photobucket

ABCD is a diamond (AD = AB = BC = CD, AD ||BC, AB ||CD), The angle A is 60 degrees. The points M and N are on the sides AB and BC accordingly.

We are given: BN+BM = AB

Prove that the triangle DMN is equilateral.

Frankly I think something is wrong with the question and we are missing a detail. But I would like a second opinion.

Thank you!