Question

Find number of possible line(s) of symmetry that triangles can have. Add these values and denote the sum by X. Similarly find the number of possible line(s) of symmetry that rectangles can have. Add these values and denote the sum by Y. Find the value of (X + Y). Your answer should be a number

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Answer 1

Let’s find X first.

Triangles can be categorized into three types:

1. Scalene Triangles: These have 0 lines of symmetry as they have all unequal sides.
2. Isosceles Triangles: These have 1 line of symmetry as two of the sides are equal.

Equilateral Triangles: These have 3 lines of symmetry as all the sides are equal in length.

This is shown in the figure.

This means a triangle can never have 2 lines of symmetry.

So, X = 0 + 1 + 3 = 4

For a rectangle, there are two lines of symmetry (as shown in the figure). The point to miss here is that all squares are rectangles too! So, a rectangle as a square can have 4 lines of symmetry as well

So, Y = 2 + 4 = 6

Which gives (X + Y) = 4 + 6 = 10