The department of triangles right into scalene, isosceles, and equilateral have the right to be thoughtof in terms of lines of symmetry. A scalene triangle is a triangle with nolines the symmetry if an isosceles triangle contends least one heat of symmetryand an equilateral triangle has three lines of symmetry. This activity providesstudents an opportunity to acknowledge these distinguishing features of the different species of triangles before the technical language has actually been introduced. Forfinding the currently of symmetry, cut-out models that the four triangles would behelpful so the the students deserve to fold lock to discover the lines.

You are watching: A triangle with exactly two lines of symmetry

This task is intended because that instruction, giving the studentswith a chance to experiment v physical models that triangles, acquiring spatialintuition through executing reflections. A word has been included at the end of the solution around why there space not other lines that symmetries for these triangles: this has been put in instance this topic comes up in a class discussion however the focus should be on identifying the suitable lines of symmetry.


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


A line of symmetry because that a triangle must go v one vertex. The two sides meeting at that vertex must be the same length in order for there to it is in a line of symmetry. When the 2 sides conference at a crest do have actually the very same length, the line of symmetry with that peak passes v the midpoint of opposing side. Because that the triangle v side lengths 4,4,3 the only possibility is to wrinkles so the 2 sides of length 4 align, so the line of the opposite goes v the vertex wherein those two sides meet. For the triangle all of whose sides have actually length 3, a proper fold through any vertex can serve as a heat of symmetry and also so there are three feasible lines. The triangle v side lengths 2,4,5 cannot have any lines that 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 two sides of size 5 meet.

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To see why there are no various other lines of symmetry because that these triangles, note that a heat of symmetry need to pass through a vertex of the triangle: if a line cut the triangle into two polygons however does no pass with a vertex, then one of those polygon is a triangle and the various other is a quadrilateral. As soon as a peak of the triangle has actually been chosen, there is only one feasible line of symmetry because that the triangle with that vertex, specific the one i m sorry goes with the midpoint of opposing side.