TopTriangle is a 2 – Dimensional figure which is bounded by three line segments. It can be of four types: Equilateral, scalene, isosceles and right angled triangle. An Equilateral Triangle is the one which is characterized by three equal sides and opposite angles of 60 degrees measure each. Lines of Symmetry in any shape are the line about which area of shape is divided into equal parts. We may have varying number of lines of symmetry in regular shapes. So question is how many lines of symmetry does an equilateral triangle have? Answer to it is 3. Three lines of symmetry can be drawn as follows:
Suppose we have an equilateral triangle ABC:
Three lines of symmetry in triangle are BF , AD and CE. These lines divide triangle in two congruent parts each:
1. For line AD triangle ABD is congruent to triangle ACD by property of Triangles SAS (SIDE, ANGLE, SIDE) with AD as common side, AB = AC and angle BAD = angle CAD.
2. For line BF triangle ABF is congruent to triangle BCF by property of triangles SAS (SIDE, ANGLE, SIDE) with BF as common side, AB = BC and angle ABF = angle CBF.
3. For line CE triangle BCE is congruent to triangle ACE by property of triangles SAS (SIDE, ANGLE, SIDE) with CE as common side, AC = BC and angle ACF = angle BCF.
Three lines we drew AD, BF and CE are considered to be perpendicular bisectors at points D, E and F respectively of three sides of triangle ABC i.e.
BD = DC,
AF = CF and,
AE = BE.