In triangle ABC with obtuse angle BAC, heights BB1 and CC1 are drawn. Prove that triangles B1AC1 and ABC are similar.
| March 9, 2021 | education
Triangles ABB1 and ACC1 are rectangular in which the angle BAB1 = CAC1 as vertical angles, then triangles ABB1 and ACC1 are similar in acute angle.
From the similarity of triangles, AC / AB = AC1 / AB1.
In triangles ABC and AB1C1 the angle ABC = B1AC1 as vertical angles, AC / AB = AC1 / AB1, then the triangles are equal in two proportional sides and the angle between them, which was required to be proved.
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