Geometrical shapes are all around us. Stand in city square and they are there. Look at trees in forest and you will find them. Even in portraitures lines play a big role in leading your viewers' eyes and in creating interest. Lines are either obvious or hidden but in both cases they can add depth to your composition.
Leading lines in architecture and cityscape photos
Look at the above photo. See how buildings on the right and left of the street converge into the main subject of the composition thus adding a three-dimensional looks and lead the eyes towards the cathedral's dome (above left) or the church (above right)? The lines in these composition create depth. They converge into the main subject of the photo being the dome of the cathedral / church. This creates a sense of distance and space. Architecture and cityscape photos are the most obvious compositions when it comes to leading lines. Leading lines can also diverge from the main subject like in the composition below.
Leading lines in landscape compositions
The most obvious advantage of using leading lines is in landscape photography because so many things are happening in the photo, you need a strong composition directly leading into your subject. Landscape composition is a bit more challenging though when it comes to identifying leading lines. Lines are not straight all the time and they are subtle in most of the time. In this landscape photo (above left) , the green and yellow grass lines are obvious leading the eyes towards the hay rolls. In the above right photo, the slightly curved road lead the eyes towards the castle standing on the hill. Those are called implied lines rather than actual lines clearly visible in architecture compositions. When shooting landscapes, take your time identifying lines, try different perspectives and crop for leading lines in post.
Leading lines in portraitures
Leading lines are also useful in portraiture but in this genre it is the subtle use of lines that make it or break it. In the examples above, the woman’s left arm and the man's both arms create lines that lead the eye up towards the faces. The lines are also visible by the tonal contrast they create against the woman's dark dress.
God created his world with geometrical shapes all around us. Circles, triangles and lines are everywhere, they are just waiting for us to discover them and use them for our advantage in photography. Keep your photos simple and clear from any clutter then add lines for a stronger and more effective composition.