Prove that the three middle lines split a triangle into four equal triangles.
August 27, 2021 | education|
The solution of the problem:
At the midpoints of the sides AB, BC, AC of the triangle ABC, mark the points K, M, O and connect them. In triangle ABC, four triangles OMC, OMK, AKO, KBM were formed.
Consider triangle AKO and triangle KBM, side AK is equal to the side KB, KO = BM, AO = KM, triangle AKO is equal to triangle KBM.
Consider the triangle KBM and OMC. Side ВМ = МС, КВ = ОМ, КМ = OC, triangle КBМ = ОМС = AKO.
Consider the OMC and OMC triangle. Side OM – common, KM = OS, KO = MС, triangle OMC = OMK = AKO = KBM.
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