The bases of the trapezoid are 24 cm and 28 cm. Calculate the length of the segment that is part of the middle line of the trapezoid and lies between its diagonals.
Let’s draw the diagonals of the trapezoid VD and AC which intersect the middle line KM at points O and E.
The diagonals of the trapezoid formed two triangles – ABC and BC.D
In the triangle ABC, the segment KE is its middle line, since AK = BK, and the segment KE is parallel to the base of the BC. The midline of a triangle is half the length of the side parallel to it. KE = BC / 2 = 24/2 = 12 cm.
Similarly, in the BCD triangle, the MO segment is the middle line of the triangle, and MO = BC / 2 = 24/2 = 12 cm.
Determine the length of the middle line of the CM.
KM = (BC + AD) / 2 = (24 + 28) / 2 = 26 cm.
Determine the length of the segment EO.
EO = KM – KE – MO = 26 – 12 – 12 = 2 cm.
Answer: The length of the segment EO = 2 cm.
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