Angles of Equilateral Triangles

Transcript

Angles of Equilateral TrianglesEquilateral triangles are those in which all the sides have equal lengths. What can we say about their angles? We can use the property Angles opposite to equal sides are equal Drawing figure Since AB = AC Angle opposite to them are equal ∴ ∠ C = ∠ B Similarly, Since AB = BC Angle opposite to them are equal ∴ ∠ C = ∠ A Thus, we can say ∠ A = ∠ B = ∠ C Now, By Angle sum property of Triangle ∠ A + ∠ B + ∠ C = 180° Since all angles are equal ∠ A + ∠ A + ∠ A = 180° 3 × ∠ A = 180° ∠ A = (180° )/3 ∠ A = 60° So, ∠ A = ∠ B = ∠ C = 60° Thus, all angles of an equilateral triangle are 60°