The diagonals AC and BD of the trapezoid of ABCD intersect at point O. The height of the trapezoid KM

| February 19, 2021 | education

The diagonals AC and BD of the trapezoid of ABCD intersect at point O. The height of the trapezoid KM is drawn through this point. Calculate its dyne if AO = 7.5 dm, AM = 6 dm, KС = 2 dm

The angle ACВ of the trapezoid of the AВСD is equal to the angle of the СAD as criss-crossing angles at the intersection of parallel lines BC and AD secant AC.

Triangles CОК and AOM are rectangular, and since the angle ОCК = OAM, the triangles are similar in acute angle.

Let’s determine the coefficient of similarity of triangles. K = СK / AM = 2/6 = 1/3 dm.

In a right-angled triangle AOM, according to the Pythagorean theorem, we determine the length of the leg OM.

OM ^ 2 = AO ^ 2 – AM ^ 2 = 56.25 – 36 = 20.25.

OM = 4.5 dm.

Then OK / OM = 1/3.

OK = OM / 3 = 4.5 / 3 = 1.5 dm.

KM = OK + OM = 1.5 + 4.5 = 6 dm.

Answer: The length of the CM height is 6 dm.



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