a A triangle with 0 lines of symmetries cannot be folded over itself in any way.
B
b Two sides have to be congruent in order for them to map onto each other when you are folding the triangle.
C
c To have two lines of symmetry, one side of the triangle has to be congruent to the other two. What do you call such a triangle and is it limited to two lines of symmetry?
D
d Use your answer from Part C.
A
aDrawing:
Type of Triangle: Scalene
B
bDrawing:
Type of Triangle: Isosceles
C
c Not possible.
D
dDrawing:
Type of Triangle: Equilateral
Practice makes perfect
a If a triangle has 0 lines of symmetry, we are unable to fold it over itself so that the two halves cover each other. A scalene triangle is an example of such a triangle. No matter how we fold it, we cannot get any of the sides to line up as they are all of different lengths.
b If a triangle has 1 line of symmetry, we can fold it over itself so that the two halves completely cover each other. This is possible if a triangle has two equal sides which is called an isosceles triangle.
c From Part B, we established that an isosceles triangle has 1 line of symmetry. For a triangle to have even 1 line of symmetry, the side you are folding over has to have the same length as the side that's not folding. Therefore, if a triangle has 2 lines of symmetry, one side has to be congruent to the other two sides.
However, notice that if one side is equal to the other two, then we can by the Transitive Property of Equality say that all three sides are equal. This means we have a third line of symmetry as well.
Therefore, we cannot draw a triangle with only two lines of symmetry.
d As explained in Part C, a triangle with three equal sides has three lines of symmetry. Therefore, by drawing an equilateral triangle, we have drawn a triangle with three lines of symmetry.
