# In an isosceles trapezoid, the diagonals are perpendicular to the height of the trapezoid 16, find its average length.

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.

Second way.

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.