The bases of the trapezoid are 3 and 14 find the largest of the line segments into which one of its diagonals
| February 28, 2021 | education
The bases of the trapezoid are 3 and 14 find the largest of the line segments into which one of its diagonals divides the middle line of this trapezoid.
Let’s draw the diagonal of the trapezoid BD which intersects the middle line KM at point O.
The diagonals of the trapezoid formed two triangles – ABD and BCD.
In triangle ABD, the segment KO is its middle line, since AK = BK, and the segment KO is parallel to the base of AD. The midline of a triangle is half the length of the side parallel to it. KO = AD / 2 = 14/2 = 7 cm.
Similarly, in the triangle BCD, the segment MO is the middle line of the triangle, and MO = BC / 2 = 2/2 = 1.5 cm.
KO> MO.
Answer: The length of the larger segment KO = 7 cm.
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