In trapezoid MNKP, the extension of the lateral sides meet at point E. and EK = EP.

univerkov | February 9, 2021 | education

In trapezoid MNKP, the extension of the lateral sides meet at point E. and EK = EP. Find the difference between the bases of the trapezoid, NK = 7cm.

Consider triangles MEP and HEK in which the angle at the vertex E is common, the angle EHK = EMP as the corresponding angles at the intersection of the parallel bases of the trapezoid MR and NC secant ME.

Then the triangles MEP and HEK are similar in two angles.

By condition, EK = KP, then EP = 2 * EK.

EK / EP = 1/2.

Then NK / MR = 1/2.

MR = 2 * NK = 2 * 7 = 14 cm.

MR – NK = 14 – 7 = 7 cm.

Answer: The base difference is 7 cm.

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