The angles at one of the bases of the trapezoid are 86 and 4, and the line segments connecting

| April 3, 2021 | education

The angles at one of the bases of the trapezoid are 86 and 4, and the line segments connecting the midpoints of the opposite sides of the trapezoid are 4 and 1. Find the base of the trapezoid.

Let ABCD be a trapezoid, AD – bases, K and L – midpoints of sides AB and CD, respectively. The sum of the angles at one of the bases is 85 + 5 = 90, so this is the larger AD base.

Extend the sides until they intersect at O.

Angle AOD = 180 – (86 + 4) = 180 – 90 = 90.

N is the middle of AD. Then ОN = AD / 2 is the median of the right-angled triangle AOD.

Since ON bisects any segment with ends on AO and DO of triangle AOD parallel to AD, it intersects BC also in its middle M.

ОМ = BC / 2.

MN = (AD – BC) / 2.

KL = (AD + BC) / 2.

AD = MN + KL.

MN = 4.

KL = 1.

AD = 4 + 1 = 5;

BC = KL – MN.

BC = 4 – 1 = 3.

Solution: 5; 3.



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