The department of triangles right into scalene, isosceles, and also equilateral can be thoughtof in terms of lines that symmetry. A scalene triangle is a triangle v nolines the symmetry if an isosceles triangle contends least one line of symmetryand an it is intended triangle has actually three present of symmetry. This activity providesstudents an possibility to recognize these differentiating features the the different varieties of triangles prior to the technical language has actually been introduced. Forfinding the currently of symmetry, cut-out models that the four triangles would certainly behelpful so the the students can fold them to uncover the lines.

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This task is intended because that instruction, giving the studentswith a opportunity to experiment through physical models that triangles, acquiring spatialintuition by executing reflections. A word has actually been added at the end of the solution about why there room not various other lines that symmetries for these triangles: this has been put in instance this topic come up in a class discussion however the emphasis should it is in on identifying the appropriate lines of symmetry.

## Solution

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

A heat of symmetry because that a triangle should go v one vertex. The two sides meeting at the vertex have to be the same size in order for there to it is in a line of symmetry. When the two sides meeting at a vertex do have actually the same length, the line of symmetry through that crest passes v the midpoint of opposing side. Because that the triangle with side lengths 4,4,3 the just possibility is to wrinkles so the two sides of length 4 align, for this reason the heat of the opposite goes with the vertex wherein those 2 sides meet. For the triangle every one of whose sides have actually length 3, a proper fold through any kind of vertex can serve as a line of symmetry and also so there room three feasible lines. The triangle through side lengths 2,4,5 can not have any kind of lines that symmetry together the next lengths are all different. Finally, the triangle with side lengths 3,5,5 has one heat of symmetry through the vertex whereby the 2 sides of length 5 meet.

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To see why there are no various other lines of symmetry for these triangles, note that a heat of symmetry must pass v a crest of the triangle: if a line cut the triangle right into two polygons yet does not pass through a vertex, then among those polygons is a triangle and the various other is a quadrilateral. As soon as a peak of the triangle has been chosen, there is only one possible line the symmetry because that the triangle with that vertex, namely the one i m sorry goes with the midpoint of the contrary side.