In an acute-angled triangle ABC, the heights AE and BD are drawn. Prove that triangle ABC is similar to triangle EDC.
| April 19, 2021 | education
In a right-angled triangle AEC, we define the cosine of the angle C.
CosC = CE / AC.
From the right-angled triangle BDC, we also determine the cosine of the angle C.
CosC = CD / BC.
Then CE / AC = CD / BC = K.
Therefore, the sides of triangles ABC and EDC are proportional.
The angle C between the proportional sides is common, then the triangles ABC and EDC are similar in two proportional sides and the angle between them, which was required to be proved.
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