The diagonals of rectangle ABCD meet at point O, point M is the midpoint of side AD. Prove that AB = 2OM.

Since ABCD is a rectangle, its diagonals, and the point of their intersection O, are divided in half.

ОВ = ОD = ВD / 2.

By condition, point M is the midpoint of side AD.

Then, in the triangle ABD, the segment OM is its midline, then OM = AB / 2, then

AB = 2 * OM, as required.

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