The base of the trapezoid is 6 and 18 cm, the diagonal divides the middle line into 2 segments.

univerkov | June 19, 2021 | education

The base of the trapezoid is 6 and 18 cm, the diagonal divides the middle line into 2 segments. Find the length of the largest of them.

Since MR is the middle line of the trapezoid, point M is the middle of its lateral side AB. The middle line of the trapezoid divides its diagonals in half, then the point H is the midpoint of the diagonal BD.

Then the segment MH, for the triangle ABD is its midline, the length of which is equal to half the length of the side of the triangle parallel to the midline.

MH = AD / 2 = 18/2 = 9 cm.

Similarly to PH, the middle line of the triangle BCD. PH = BC / 2 = 6/2 = 3 cm.

Answer: The length of the larger segment is 9 cm.

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