In trapezoid ABCD, the continuation of the sides intersect at point K, and point B is the midpoint of the segment AK.
| February 16, 2021 | education
In trapezoid ABCD, the continuation of the sides intersect at point K, and point B is the midpoint of the segment AK. Find the sum of the bases of the trapezoid if AD = 12 cm.
Consider a triangle AKD, in which, according to the condition, point B is the middle of the segment AK, that is, AB = BK, and since BC is parallel to AD, as the base of the trapezoid, then the segment BC is the middle line of the triangle.
The length of the midline of a triangle is half the length of the side parallel to it.
BC = AD / 2 = 12/2 = 6 cm.
Since the middle line of the triangle coincides with the small base of the trapezoid, the sum of the sides of the trapezoid will be 12 + 6 = 18 cm.
Answer: The sum of the bases of the trapezoid is 18 cm.
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