In an isosceles trapezoid ABCD with bases AD and BC. CK – height, AK = 8 cm. Find the middle line of the trapezoid.

univerkov | September 6, 2021 | education

We draw the height of the ВM. If the trapezoid is isosceles, then AM = KD, and BC = MK. We denote AM = KD = x (cm), then MK = 8 – x (cm), then, respectively, BC = 8 – x (cm). Let’s draw the middle line of the trapezoid NF. Let’s write down the formula for finding the middle line NF = (BC + AD) / 2. (The middle line is equal to the sum of the bases divided by two). Substitute the expressions for the bases of the trapezoid into this formula: BC = 8 – x, AD = AM + MK + KD = x + 8-x + x = 8 + x.
NF = ((8-x) + (8 + x)) / 2 = 16/2 = 8 (cm).

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