Single-crystalline, hexagon shaped lead halide perovskite microplates have been synthesized and their lasing actions have attracted intensive research attention. However, up to now, only the hexagonal whispering gallery modes (WGMs) have been experimentally observed. The dominant high Q modes, the triangular WGMs, are still surprisingly absent. Herein we study the mechanisms of forming different WGMs. We show that tiny nanoparticles can strongly affect the lasing modes in hexagonal cavities. In addition, we also explore a simple way to selectively excite the triangular WGMs in hexagon shaped microplates. By introducing either one-dimensional or rotational parity-time (PT) symmetry into the hexagonal microdisk, the hexagonal WGMs experience balanced gain and loss and cannot lase until their PT symmetries are broken. The triangular WGMs show quite different behaviors due to their unique field distributions. The modes along one triangular orbit are mostly confined within the gain region, whereas the modes along the other triangular orbit are mostly localized within the loss area. Then the PT symmetries of triangular WGMs are naturally broken and one set of triangular WGMs can lase very quickly. Consequently, only triangular WGMs can be excited in lasing experiments. We believe our research will be important for tailoring and understanding the lasing actions in hexagon shaped microcavities.