In an isosceles trapezoid, the height divides the larger base into segments equal

In an isosceles trapezoid, the height divides the larger base into segments equal to 6 and 14 cm. Find the middle line of the trapezoid.

Given:
ABCE is an isosceles trapezoid,
BО – height,
AO = 6 centimeters,
OE = 14 centimeters.
Find the midline of a trapezoid, that is, KH -?
Solution:
1) Consider an isosceles trapezoid ABCE. Let’s draw the height of CM.
2) The right-angled triangles ABO and CME are equal in hypotenuse and acute angles, since AB = CE and the angle BAO = CEM from the definition of an isosceles trapezoid. Then AO = ME = 14 – 6 = 8 (centimeters);
3) KH = 1/2 * (BC + AE);
OM = BC = 8 centimeters;
KH = 1/2 * (8 + 20);
KH = 1/2 * 28;
KH = 14 centimeters.
Answer: 14 centimeters.