Evolutionary Biologists are often faced with the need to compare phylogenetic trees. One popular method consists in visualizing the trees face to face with links connecting matching taxa. These tanglegrams are optimized beforehand so that the number of lines crossing (the entanglement) is minimal. This representation is implicitly justified by the expectation that the level of entanglement is correlated with the level of similarity (or congruence) between the trees compared. Using simulations, we show that this correlation is actually very weak, which should preclude the use of such technique for getting insight into the level of congruence between trees.