The department of triangles into scalene, isosceles, and also equilateral have the right to be thoughtof in terms of lines of symmetry. A scalene triangle is a triangle with nolines that symmetry while an isosceles triangle has at least one line of symmetryand an equilateral triangle has three lines of symmetry. This activity providesstudents an possibility to recognize these differentiating features that the different types of triangles prior to the technological language has been introduced. Forfinding the currently of symmetry, cut-out models that the four triangles would certainly behelpful so the the students can fold castle to discover the lines.

You are watching: Triangle with no lines of symmetry

This task is intended for instruction, offering the studentswith a possibility to experiment v physical models that triangles, acquiring spatialintuition through executing reflections. A word has been added at the finish of the solution about why there space not other lines the symmetries because that these triangles: this has been inserted in situation this topic comes up in a course discussion however the emphasis should it is in on identify the appropriate lines that symmetry.

## Solution

The currently of symmetry because that the 4 triangles are indicated in the picturebelow:

A line of symmetry for a triangle must go with one vertex. The two sides conference at that vertex should be the same size in order for there to it is in a line of symmetry. When the two sides conference at a peak do have the exact same length, the heat of symmetry through that peak passes with the midpoint of the contrary side. For the triangle with side lengths 4,4,3 the only possibility is to wrinkles so the two sides of length 4 align, for this reason the heat of symmetry goes through the vertex wherein those two sides meet. For the triangle every one of whose sides have actually length 3, a suitable fold through any vertex have the right to serve together a heat of symmetry and also so there are three possible lines. The triangle with side lengths 2,4,5 cannot have any type of lines of symmetry as the next lengths room all different. Finally, the triangle through side lengths 3,5,5 has one line of symmetry with the vertex where the 2 sides of length 5 meet.

See more: What Number Is Halfway Between 37 And 143 ? What Number Is Halfway Between 37 And 143

To watch why there room no other lines the symmetry because that these triangles, keep in mind that a heat of symmetry need to pass v a vertex of the triangle: if a line cut the triangle right into two polygons but does not pass through a vertex, then among those polygon is a triangle and the various other is a quadrilateral. Once a peak of the triangle has been chosen, there is just one possible line that symmetry for the triangle with that vertex, specific the one i beg your pardon goes through the midpoint of the contrary side.