The diagonals of the trapezoid divide its midline into segments of length which are related as 3 2 3

| August 22, 2021 | education

The diagonals of the trapezoid divide its midline into segments of length which are related as 3 2 3 find the ratio of the bases of the trapezoid.

Let the trapezoid ABCD be given, and its middle line MK.
Consider triangles BCD and ABC. Considering that the part of the midline of triangles ABC and BCD is equal to 3 units, then the smaller base of the trapezoid BC is equal to 3 * 2 = 6 (units).
Now consider triangles ABD and ACD. In them, the middle line is (2 + 3) units = 5 units. Hence, the base AD = 5 * 2 = 10 (units).
Now we find the ratio of the bases of the trapezoid: BC / AD = 6/10 = 3/5. Check: MK = (BC + AD) / 2 = (6 + 10) / 2 = 8 = (2 + 3 + 2).

The solution uses the property of the midline of the triangle: the midline of the triangle is equal to half of the base of the triangle.



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