Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precise multi-step symbolic deduction. Although test-time scaling (TTS) has demonstrated remarkable success in general mathematical reasoning, it fails to scale effectively under the symbolic-program paradigm for plane geometry. We identify two key obstacles: limited reasoning diversity induced by rigid symbolic programs and insufficient explicit visual grounding before symbolic deduction. To address these issues, we propose Multi-Trace Synthesis (MTS), which converts each symbolic program into heterogeneous reasoning traces, including executable Python scripts and CoT-augmented variants. We further propose Perception-Augmented (PA) training, which parses diagrams into structured semantic clauses before deduction, and Consensus-Guided Multi-Trace Ensemble (CG-MTE) for efficient self-adaptive inference. Experiments on three geometry benchmarks show that our method consistently improves PGP-solving across model scales and achieves strong performance against both general-purpose MLLMs and specialized geometry solvers. Under test-time scaling, CG-MTE achieves a comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8×. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.

Solving math word problem (MWP) with AI techniques has recently made great progress with the success of deep neural networks (DNN), but it is far from being solved. We argue that the ability of learning by analogy is essential for an MWP solver to better understand same problems which may typically be formulated in diverse ways. However most existing works exploit the shortcut learning to train MWP solvers simply based on samples with a single question. In lack of diverse questions, these methods merely learn shallow heuristics. In this paper, we make a first attempt to solve MWPs by generating diverse yet consistent questions/equations. Given a typical MWP including the scenario description, question, and equation (i.e., answer), we first generate multiple consistent equations via a group of heuristic rules. We then feed them to a question generator together with the scenario to obtain the corresponding diverse questions, forming a new MWP with a variety of questions and equations. Finally we engage a data filter to remove those unreasonable MWPs, keeping the high-quality augmented ones. To evaluate the ability of learning by analogy for an MWP solver, we generate a new MWP dataset (called DiverseMath23K) with diverse questions by extending the current benchmark Math23K. Extensive experimental results demonstrate that our proposed method can generate high-quality diverse questions with corresponding equations, further leading to performance improvement on Diverse-Math23K. The code and dataset is available at: https://github.com/zhouzihao501/DiverseMWP.