The height of an isosceles trapezoid drawn from the vertex C divides the base AD

univerkov | January 6, 2021 | education

The height of an isosceles trapezoid drawn from the vertex C divides the base AD into segments of length 1 and 17. Find the length of the base BC.

Let’s build from the top В to the height of the ВК.
Since VK and CH are the heights of the trapezoid, then the quadrilateral ВСНK is a rectangle, then BC = KН, and the triangles AВK and СDН are rectangular.
In right-angled triangles AВK and СDН AВ = СD, since the trapezoid is isosceles, ВK = CH as the height of the trapezoid, then the triangles are equal in leg and hypotenuse, which means AK = DН = 1 cm.
KН = ВС = AD – AK – DН = 18 – 1 – 1 = 16 cm.
Answer: The base length of the BC is 16 cm.

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