The division of triangles into scalene, isosceles, and also equilateral can be thoughtof in terms of lines the symmetry. A scalene triangle is a triangle through nolines of symmetry if an isosceles triangle contends least one heat of symmetryand an equilateral triangle has three present of symmetry. This activity providesstudents an chance to recognize these separating features of the different types of triangles prior to the technological language has actually been introduced. Forfinding the present of symmetry, cut-out models that the 4 triangles would behelpful so the the students can fold lock to find the lines.

You are watching: How many lines of symmetry does an equilateral triangle have

This task is intended for instruction, giving the studentswith a opportunity to experiment v physical models the triangles, obtaining spatialintuition through executing reflections. A word has actually been included at the finish of the solution about why there are not various other lines of symmetries for these triangles: this has been put in instance this topic come up in a class discussion but the focus should be on identify the appropriate lines of symmetry.

## Solution

The present of symmetry for the four triangles are indicated in the picturebelow: A line of symmetry because that a triangle should go through one vertex. The 2 sides conference at that vertex need to be the same size in order because that there to be a line of symmetry. When the two sides conference at a vertex do have actually the very same length, the heat of symmetry v that vertex passes v the midpoint of opposing side. Because that the triangle v side lengths 4,4,3 the just possibility is to fold so the two sides of size 4 align, therefore the line of symmetry goes with the vertex wherein those 2 sides meet. For the triangle all of whose sides have actually length 3, a suitable fold through any vertex deserve to serve together a line of symmetry and so there room three possible lines. The triangle v side lengths 2,4,5 can not have any kind of lines of symmetry as the next lengths are all different. Finally, the triangle with side lengths 3,5,5 has one line of symmetry v the vertex wherein the 2 sides of size 5 meet.

See more: Can You Take Tylenol With Zyrtec, Can You Take Zyrtec And Tylenol Cold Together

To see why there are no various other lines that symmetry because that these triangles, keep in mind that a heat of symmetry should pass with a crest of the triangle: if a line cut the triangle right into two polygons but does no pass through a vertex, then among those polygons is a triangle and the various other is a quadrilateral. When a peak of the triangle has been chosen, there is just one feasible line the symmetry because that the triangle through that vertex, namely the one which goes with the midpoint of the opposite side.