The base of the trapezoid is 10 and 11. Find the largest of the line segments into which one of its diagonals

| May 7, 2021 | education

The base of the trapezoid is 10 and 11. Find the largest of the line segments into which one of its diagonals divides the middle line of this trapezoid.

A trapezoid is a quadrilateral with two parallel and two non-parallel sides. The parallel sides are called the bases of the trapezoid, and the second two are called the sides.

Consider a trapezoid ABCD, in which BC and AD are bases and are respectively equal to 10 and 11, MK is the middle line, O is the intersection of AC and MK.

Consider two triangles ABC and ACD. In triangle ABC MO is the middle line of the triangle, MO = 1/2 * BC = 10/2 = 5. In triangle ACD OK is the middle line of the triangle, OK = 1/2 * AD = 11/2 = 5.5.

Answer: the largest of the segments into which one of its diagonals divides the middle line of the trapezoid is the segment OK = 5.5.



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