In the trapezoid MNKP, the extension of the lateral sides intersect at point E with EK = KP. find the difference between

In the trapezoid MNKP, the extension of the lateral sides intersect at point E with EK = KP. find the difference between the bases of the trapezoid if NK = 7 cm.

Since, by condition, the segments EK and KP are equal, the point K is the midpoint of the segment EP.

At the trapezoid, the bases are parallel, the NK segment is parallel to the PM, then the NK segment is the midline of the MEP triangle, and therefore its length is equal to half the length of the MP base.

Then MP = 2 * NK = 2 * 7 = 14 cm.

Then МР – НК = 14 – 7 = 7 cm.

Answer: The difference between the bases of the trapezoid is 7 cm.