The department of triangles into scalene, isosceles, and equilateral can be thoughtof in terms of lines the symmetry. A scalene triangle is a triangle through nolines of symmetry when an isosceles triangle contends least one heat of symmetryand an equilateral triangle has three lines of symmetry. This activity providesstudents an opportunity to recognize these distinguishing features that the different varieties of triangles prior to the technical language has been introduced. Forfinding the currently of symmetry, cut-out models the the 4 triangles would certainly behelpful so that the students deserve to fold lock to uncover the lines.

You are watching: A triangle with more than one line of symmetry

This job is intended for instruction, giving the studentswith a possibility to experiment with physical models of triangles, gaining spatialintuition by executing reflections. A word has been included at the end of the solution about why there are not various other lines of symmetries because that these triangles: this has actually been put in case this topic comes up in a class discussion but the emphasis should it is in on identify the ideal lines that symmetry.

## Solution

The lines of symmetry because that the 4 triangles are suggested in the picturebelow: A heat of symmetry for a triangle should go through one vertex. The 2 sides conference at the vertex should be the same size in order for there to be a line of symmetry. Once the two sides conference at a peak do have actually the same length, the heat of symmetry with that peak passes v the midpoint of the opposite side. Because that the triangle through side lengths 4,4,3 the only possibility is to wrinkles so the 2 sides of length 4 align, so the heat of the contrary goes through the vertex wherein those two sides meet. For the triangle all of whose sides have length 3, a proper fold through any type of vertex can serve together a line of symmetry and also so there room three feasible lines. The triangle v side lengths 2,4,5 can not have any type of lines of symmetry together the side lengths space all different. Finally, the triangle through side lengths 3,5,5 has actually one line of symmetry with the vertex whereby the 2 sides of size 5 meet.

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To view why there are no various other lines that symmetry because that these triangles, keep in mind that a heat of symmetry must pass with a vertex of the triangle: if a line cut the triangle into two polygons however does no pass v a vertex, then among those polygon is a triangle and also the other is a quadrilateral. When a vertex of the triangle has been chosen, over there is just one feasible line the symmetry for the triangle through that vertex, specific the one i m sorry goes through the midpoint of opposing side.