The bases of a trapezoid are equal to 3 and 6. Find the largest of the line segments
| September 21, 2021 | education
The bases of a trapezoid are equal to 3 and 6. Find the largest of the line segments into which one of its diagonals divides the middle line of this trapezoid.
Consider the drawing. MN is the middle line of the trapezoid. It connects the midpoints of the sides and passes through the point O, which is the midpoint of the trapezoid diagonal (by Thales’ theorem). MO will be the midline of triangle ABC, and ON will be the midline of triangle ACD. The midline of the triangle is parallel to the base and equal to half of it.
MO = 1/2 * BC; MO = 1/2 * 3 = 1.5.
ON = 1/2 * AD; ON = 1/2 * 6 = 3.
Larger segment – ON = 3.
Answer. 3.
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