The bisectors of angles A and B at the lateral side AB of the trapezoid ABCD meet at point F.

| May 14, 2021 | education

The bisectors of angles A and B at the lateral side AB of the trapezoid ABCD meet at point F. The bisectors of angles C and D at the lateral side CD meet at point G. Find FG if the bases are 16 and 30, the sides are 13 and 15.

The bisectors of the corners of the trapezoid, drawn from the vertices of the lateral sides, intersect at right angles, and the point of their intersection lies on the midline of the trapezoid. Then triangles BFA and CGD are rectangular, and points F and G belong to the middle line of the trapezoid KM. Determine the length of the middle line of the trapezoid KM = (BC + AD) / 2 = (16 + 30) / 2 = 46/2 = 23 cm.

Since KM is the middle line, then FM and GK are the medians of right-angled triangles drawn from a right angle to the hypotenuse. Then FM = AB / 2 = 13/2 = 6.5 cm, GK = CD / 2 = 15/2 = 7.5 cm.

Then FG = MK – FM – GK = 23 – 6.5 – 7.5 = 9 cm.

Answer: The length of the segment FG is 9 cm.



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