Given a trapezoid OKMN (ON – larger base). The sides of the trapezoid are extended to the intersection

| June 25, 2021 | education

Given a trapezoid OKMN (ON – larger base). The sides of the trapezoid are extended to the intersection at point S. 1) Prove that triangle SON is similar to triangle SKM. 2) Find the base ON if: a) SK = 8, OK = 4, KM = 18 b) MS = 14, MN = 7 , KM = 12

In triangles SOH and SKM, the angle S is common, the angle SKM = SOH as the corresponding angles at the intersection of the parallel lines OH and KM of the secant OS, then the triangles SOH and SKM are similar in two angles, which was required to prove.

Side length SO = SK + OK = 8 + 4 = 12 cm, then the coefficient of similarity is: K = SK / SO = 8/12 = 2/3.

Then OH = KM * 3/2 = 18 * 3/2 = 27 cm.

Side length SN = SM + MH = 14 + 7 = 21 cm, then the coefficient of similarity is: K = SM / SN = 14/21 = 2/3.

Then OH = KM * 3/2 = 12 * 3/2 = 18 cm.

Answer: The length of the OH base is 27 cm and 18 cm.



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