The basic image of the triangle is probably the pyramid, and this has been a constant and major element in many compositions in painting (just as much as in sculpture and architecture) ever since.
Some are quite obvious, like this exemple from the 18th century French painter Chardin, others need to be looked at more closely, like the painting below, by Piero della Francesca, in Tuscany of the 15th century.
To understand the structure of some paintings, it often helps to draw lines between key points of the major elements, which may or may not be important in terms of size, but are always important in terms of signification, as in this example from Valasquez:
What is it about the triangle, and the pyramidical form, that makes it so profoundly satisfying to the eye? I suppose it is a balance between stability and the feeling of hamony engendered by that, and the more dynamic sensations given by the vertical axis and the sharp corners. The stability can be more or less precarious, depending on the relationship between the base and the height of the triangle.
The triangle was a favourtite compositional tool for Cézanne, as the well-known images of the Mont Saint Victoire show clearly. Of course part of this derived from the shape of the mountain itself, but virtually all the forms within the landscape below are also broken down into more or less triangular elements, which act like echos of the main subject, giving the painting a kind of permanent vibration that surges from the form as much as from the colour. Cubism took this further in a way, but in my opinion with less subtlety, as in all forms of systemisation, where the process takes over too much.
Of course abstract art has also widely used the triangle, like this example from James Tyrrell, which gives me something quite close to the sensations I have when looking at the pyramids, some 4000 years older! What is new?