The bases of the trapezoid are 2 and 8 cm. Find the segments of the midline into which it is divided by the diagonals.
| February 6, 2021 | education
Determine the length of the middle line KН of the trapezium AВСD.
KН = (BC + AD) / 2 = (2 + 8) / 2 = 10/2 = 5 cm.
In the ABC triangle, the KM segment is parallel to the BC, point K is the middle, then the KM is the middle line of the ABC triangle, which means KM = BC / 2 = 2/2 = 1 cm.
In the ВСD triangle, similarly, the PH segment is its midline, then ВН = BC / 2 = 2/2 = 1 cm.
The length of the segment МР = КН – КМ – РН = 5 – 1 – 1 = 3 cm.
Answer: The diagonals divide the middle line into segments of 1 cm, 3 cm, 1 cm.
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