The bisectors of obtuse angles of an isosceles trapezoid intersect at a point lying on the greater base of the trapezoid.

univerkov | December 12, 2020 | education

The bisectors of obtuse angles of an isosceles trapezoid intersect at a point lying on the greater base of the trapezoid. The smaller base of the trapezoid is 8 cm, and the side 9 cm. Find the middle line of the trapezoid.

In an isosceles triangle, the bisectors of the angles cut off the isosceles triangles.
The AВK triangle is isosceles, AB = AK, the СDK triangle is isosceles, DС = DC. Since AB = SD = 9 cm, then AK = DK = 9 cm, and then AD = AK + DK = 9 + 9 = 18 cm.
Let’s define the middle line of the trapezoid.
MK = (BP + BC) / 2 = (18 + 8) / 2 = 13 cm.
Answer: The middle line of the trapezoid is 13 cm.

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