# What is a linear symmetry?

*It is called line symmetry when we can actually draw a
line down the middle of a figure that divides the figure into two
mirror images.*

### What is the linear relationship between number of sides and number of lines of symmetry?

If you're talking about convex polygons with equal sides (eg. equilateral triangles, squares, pentagons, hexagons, etc.), then the relationship is a very direct one. In those cases, there are as many lines of symmetry as there are points in the polygons. A triangle has three lines of symmetry, a square has four, a pentagon five, etc.

### How is a molecular orbital formed?

In molecular orbital theory, MO theory, molecular orbitals are "built" from atomic orbitals. A common approach is to take a linear combination of atomic orbitals (LCAO), specifically symmetry adapted linear combinations (SALC) using group theory. The formation of a bond is essentially down to the overlap of the orbitals, the orbitals being of similar energy and the atomic orbital wave functions having the correct symmetry.

### How do you find linear symmetry of polygon?

For a polygon with an even number of vertices join each vertex to the opposite vertex. Test for symmetry. join the mid-point of each side to the mid-point of the opposite side. Test for symmetry. For a polygon with an odd number of vertices join each vertex to the mid-point of the opposite side. Test for symmetry.

### How do you sketch a figure with rotational symmetry but no line symmetry?

When a shape is rotated about its centre, if it comes to rest in a position and looks exactly like the original, then it has rotational symmetry. A shape like an equilateral triangle would therefore have an order of rotational symmetry of 3. The general rule for a regular polygon (shapes such as pentagons, heptagons, octagons etc. is, that the number of sides is the same as the number of lines of symmetry, which is…