In an isosceles trapezoid, the diagonals, at the point of intersection, are divided into equal segments.
ОВ = ОС, ОА = ОD. Since the diagonals intersect at right angles, the triangle AOD is rectangular and isosceles, then the angle OAD = ODA = (180 – 90) / 2 = 45.
The AOH triangle is rectangular, and since the angle OAН = 45, the triangle is also isosceles, AH = OH = AD / 2, since OH is the height and median of the triangle AOD.
Similarly, in the triangle BOK, OK = BK = BC / 2.
Then KH = OK + OH = AD / 2 + BC / 2 = (AD + BC) / 2, which is the middle line of the trapezoid.
MP = KH = 16 cm.
If in an isosceles trapezoid the diagonals intersect at right angles, then the middle line of the trapezoid is equal to its height. MP = KH = 16 cm.
Answer: The middle line of the trapezoid is 16 cm.
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