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are two triangles similar?

Source: Sharygin contest. The final raund. 2008. Grade 8. First day. Problem 5

August 31, 2008
geometry unsolvedgeometry

Problem Statement

(A.Zaslavsky) Given two triangles ABC ABC, A′B′C′ A'B'C'. Denote by α \alpha the angle between the altitude and the median from vertex A A of triangle ABC ABC. Angles β \beta, γ \gamma, α′ \alpha', β′ \beta', γ′ \gamma' are defined similarly. It is known that \alpha \equal{} \alpha', \beta \equal{} \beta', \gamma \equal{} \gamma'. Can we conclude that the triangles are similar?
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