The diagonals of the trapezoid MP and NK intersect at point O. ON = 9cm OK = 12cm MK = 24cm Find: NP?

Let us prove that the HOP triangle is similar to the MOC triangle.

Ugo HOK = MOK as vertical angles at the intersection of the diagonals HK and MР.

Angle ОНР = OKM as criss-crossing angles at the intersection of parallel straight lines HP and MK of the secant NC.

Then the triangles HOP and MOK are similar in two angles.

Determine the coefficient of similarity of triangles.

OH / OK = 9/12 = 3/4.

Then HP / MK = 3/4.

HP = 3 * MK / 4 = 3 * 24/4 = 18 cm.

Answer: The length of the base of the HP is 18 cm.