Prove that the distances from the vertices of an equilateral triangle to the lines containing the opposite sides are equal
August 28, 2021 | education|
The distance from the top to the opposite side is the perpendicular.
Let’s designate this equilateral triangle ABC, draw the heights: AH, BK, CM.
Consider right-angled triangles ABK, AСН, BСК, in them:
– hypotenuse (side of an equilateral triangle) AB = BC = AC.
– ∠ A = ∠ B = ∠ C = 60 ° (angles of an equilateral triangle).
Received one of the signs of equality of right-angled triangles – by hypotenuse and acute angle.
Equality of triangles implies equality of all sides and angles.
AH = BK = CM.
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