Question

How many lines of symmetry are there for an equilateral triangle?

Answer 1

Hint:
The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry. A scalene triangle is a triangle with no lines of symmetry which isosceles triangle has at least one line of symmetry. Thus activity provides students an opportunity to recognize their distinguishing features, before the technical language has been introduced. For finding the lines of symmetry, cut-out methods of the four triangles would be helpful so that the students can tell them to find the lines.

Complete step by step solution:
Step – 1: In geometry, a line of symmetry of a given shape is a line that can be drawn on the shape in such a way that it uplifts the shape into two congruent shapes or shapes of the exact same shape and exact same size.
Step – 2 : It is possible for shapes to have no lines of symmetry, a finite number of lines of symmetry, or a infinite amount of lines of symmetry’; it all depends on the shape that one is working with.

Step – 3 :
An equilateral triangle, or a triangle in which all of the sides have equal length, has three lines of symmetry.

Note:
An equilateral triangle has rotational symmetry of order $3$. It has three equal sides. All these angles are equal. In the equilateral triangle, all the three angles are ${60^0}$.
A line of symmetry for a triangle must go through one vertex. The two sides meeting at that vertex must be the same length in order for there to be a line of symmetry.