Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts (N = 44) were asked to judge the truth and to justify their judgments for four geometry conjectures. Videotaped interviews were transcribed and coded for occurrences of gestures and speech during the proof production process. Analyses provide empirical support for claims that geometry proof production is an embodied activity, even when controlling for math expertise, language use, and spatial ability. "Dynamic depictive gestures" portray generalizable properties of shape and space through enactment of transformational operations (e.g., dilation, skewing). Occurrence of dynamic depictive gestures and nondynamic depictive gestures are associated with proof performance, insight, and intuition, as hypothesized, over and above contributions of spoken language. Geometry knowledge for proof may be embodied and accessed and revealed through actions and the transformational speech utterances describing these actions. These findings have implications for instruction, assessment of embodied knowledge, and the design of educational technology to facilitate mathematical reasoning by promoting and tracking dynamic gesture production and transformational speech.