The division of triangles right into scalene, isosceles, and equilateral deserve to be thoughtof in terms of lines the symmetry. A scalene triangle is a triangle v nolines of symmetry if an isosceles triangle has at least one line of symmetryand an equilateral triangle has actually three currently of symmetry. This activity providesstudents an chance to identify these differentiating features the the different species of triangles before the technical language has been introduced. Forfinding the present of symmetry, cut-out models that the 4 triangles would certainly behelpful so that the students can fold castle to uncover the lines.

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This task is intended because that instruction, giving the studentswith a chance to experiment v physical models the triangles, gaining spatialintuition by executing reflections. A word has been included at the end of the solution around why there are not other lines of symmetries because that these triangles: this has actually been inserted in case this topic comes up in a class discussion however the emphasis should be on identifying the ideal lines of symmetry.

## Solution

The lines of symmetry for the four triangles are indicated in the picturebelow:

A line of symmetry for a triangle must go v one vertex. The two sides conference at that vertex must be the same size in order for there to be a heat of symmetry. When the two sides meeting at a crest do have the same length, the heat of symmetry through that crest passes v the midpoint of opposing side. For the triangle with side lengths 4,4,3 the only possibility is to fold so the two sides of length 4 align, therefore the heat of the contrary goes v the vertex where those two sides meet. For the triangle every one of whose sides have actually length 3, a suitable fold through any kind of vertex have the right to serve together a heat of symmetry and so there space three possible lines. The triangle with side lengths 2,4,5 can not have any lines the symmetry together the next lengths are all different. Finally, the triangle with side lengths 3,5,5 has one line of symmetry with the vertex wherein the 2 sides of length 5 meet.

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To check out why there are no other lines of symmetry because that these triangles, note that a line of symmetry should pass with a vertex of the triangle: if a line cut the triangle right into two polygons but does not pass with a vertex, then one of those polygon is a triangle and also the various other is a quadrilateral. When a crest of the triangle has been chosen, there is just one feasible line that symmetry because that the triangle through that vertex, namely the one which goes v the midpoint of the opposite side.