# 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.

Q.E.D.

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