Large Language Models (LLMs) face challenges in integrating linguistic and spatial reasoning, which limits their performance on geometry problems. While prior work has attempted to bridge this gap using diagram parsers with multimodal models, a systematic comparison of how various auxiliary modalities and their combinations affect performance has been lacking. To address this, we present a systematic study of four auxiliary modalities—formal diagram facts (CDL), natural language representations (T_CDL), diagram descriptions (DES), and image augmentations (IMG)—on a range of open- and closed-source multimodal LLMs. Our analysis reveals a compelling dichotomy in the effectiveness of these modalities. While formal representations like CDL and T_CDL offer a modest performance lift, diagram descriptions (DES) cause a dramatic split: they significantly boost the accuracy of open-source LLMs which often struggle with visual parsing, while often misleading more capable closed-source models and causing a performance drop. This highlights a critical trade-off between augmenting input with helpful information and introducing misleading noise, demonstrating that the efficacy of auxiliary modalities is heavily dependent on the inherent capabilities of the underlying model.

Recent advances in large language models (LLMs) have significantly improved mathematical problem-solving. Among various techniques, paraphrasing problem statements has emerged as a promising strategy to enhance model understanding and accuracy.We define twelve paraphrasing types grounded in mathematics education theory and analyze their impact on LLM performance across different configurations. To automate selection, we propose a Paraphrase Type Selector that predicts effective paraphrases for each problem.Experiments on MATH-500, SVAMP, and AIME shows consistent performance gain from paraphrased problems. On MATH-500 with LLaMA 3.1-8B, combining the original with the best five paraphrased problems improves accuracy by +8.4%, with the selector achieving an additional +1.33% gain.