The bases of the trapezoid are 6 cm and 10 cm, and the sides are 2 cm and 4 cm. The bisectors of the corners

| February 25, 2021 | education

The bases of the trapezoid are 6 cm and 10 cm, and the sides are 2 cm and 4 cm. The bisectors of the corners at one side intersect at point A, and the other at point B, find AB.

The sum of the angles of the trapezoid at its lateral side is 180, and since the PR and EA are the bisectors, the sum of the angles EPR + AEB = 90, then the angle EAP = 90, and the EAP triangle is rectangular. According to the property of the bisector of the angle, the REB triangle is isosceles, EP = EP = 4 cm, and then the bisector EA is also its median, then AP = AP.

Similarly, in the triangle OLD B, the bisector is the height and the median, and DO = DL = 2 cm.

Extend AB to the intersection with EP and DL.

Then KM is the middle line of the trapezoid, AK is the middle line of the EPВ triangle, ВM is the middle line of the ODL triangle.

KM = (PL + ED) / 2 = 16/2 = 8 cm.

AK = EP / 2 = 4/2 = 2 cm.

BM = OD / 2 = 2/2 = 1 cm.

AM = KM – AK – BM = 8 – 2 – 1 = 5 cm.

Answer: The length of the segment AM is 5 cm.



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