The heights of an acute-angled triangle AA1 and BB1 meet at point E. Prove that angles AA1B1 and ABB1 are equal.
| August 14, 2021 | education
Triangles AEB1 and BEA1 are rectangular, in which the angle AEB1 = BEA1 as the vertical angles at the intersection of the heights BB1 and AA1.
From the similarity of triangles EB1 / EA1 = AE / BE.
In triangles EA1B1 and AEB, the angle A1EB1 = AEB as vertical angles, then triangles EA1B1 and AEB are similar in two proportional sides and the angle between them.
Then the angle ЕА1В = ABE as similar angles of similar triangles, and then the angle AA1B1 = ABB1, which was required to prove.
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