The division of triangles right into scalene, isosceles, and equilateral deserve to be thoughtof in terms of lines of symmetry. A scalene triangle is a triangle through nolines that symmetry when an isosceles triangle contends least one line of symmetryand an it is intended triangle has three currently of symmetry. This activity providesstudents an opportunity to recognize these separating features the the different types of triangles before the technological language has actually been introduced. Forfinding the currently of symmetry, cut-out models that the 4 triangles would behelpful so that the students can fold them to discover the lines.

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This job is intended because that instruction, giving the studentswith a chance to experiment v physical models that triangles, getting spatialintuition through executing reflections. A word has actually been added at the end of the solution around why there room not other lines of symmetries for these triangles: this has actually been inserted in instance this topic come up in a course discussion however the emphasis should be on identify the appropriate lines of symmetry.

## Solution

The currently of symmetry for the 4 triangles are shown in the picturebelow: A line of symmetry because that a triangle should go v one vertex. The 2 sides conference at that vertex must be the same size in order for there to be a heat of symmetry. As soon as the 2 sides conference at a vertex do have actually the exact same length, the heat of symmetry v that crest passes through the midpoint of the opposite side. For the triangle through side lengths 4,4,3 the only 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 every one of whose sides have length 3, a appropriate fold through any type of vertex can serve together a line of symmetry and also so there space three possible lines. The triangle through side lengths 2,4,5 can not have any lines the symmetry as the next lengths are all different. Finally, the triangle v side lengths 3,5,5 has one line of symmetry v the vertex where the 2 sides of size 5 meet.

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To view why there space no various other lines of symmetry for these triangles, note that a line of symmetry have to pass through a peak of the triangle: if a line cuts the triangle into two polygons but does not pass v a vertex, then one of those polygons is a triangle and also the other is a quadrilateral. As soon as a crest of the triangle has actually been chosen, there is just one possible line that symmetry because that the triangle v that vertex, namely the one i beg your pardon goes with the midpoint of opposing side.