The diagonal of the trapezoid divides the midline into 4 cm and 9 cm segments. Find the base of the trapezoid.

univerkov | January 15, 2021 | education

The diagonal of the trapezoid divides it into two triangles: ΔABС and ΔAСD.
The segments KO and OM, into which the middle line of the trapezoid is divided, are the midlines of these triangles.
The bases of the trapezoid are the bases of the triangles, therefore they are equal to twice the length of their midlines:
KO = BC / 2;
BC = 2 KO;
BC = 4 2 = 8 cm.
OM = AD / 2;
AD = 2 · ОМ;
AD = 9 2 = 18 cm.
Answer: the bases of the trapezoid are 8 cm and 18 cm.

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