This article explores the use of Extended Reality (XR) technologies, such as Augmented Reality (AR) and motion capture, in mathematics instruction, specifically focusing on geometry learning. Our research highlights the challenges students face in learning geometry due to its abstract nature and the potential of XR technologies to create interactive and immersive learning experiences. We emphasize the role of embodied learning and gestures in mathematics education and how XR technologies can support equitable teaching practices. The embodied motions in XR allows for knowledge to be instantiated in physical ways, positioning all students as competent doers of mathematics. Our research shows how methods of teaching mathematics with XR technologies can reveal important student understandings and highlight how students and teachers can build on each other's reasoning. Students engage in discourse using speech, body movements, and gestures in these immersive environments. Two case illustrations are provided to demonstrate the power of XR technologies in teaching geometry. The first case involves high school students creating arm motions to represent geometry conjectures in a motion capture game, while the second case involves students using AR goggles to manipulate holograms of geometric figures. This article concludes with recommendations for teachers and researchers to incorporate gestures in mathematics instruction and leverage XR technologies to enhance students' understanding of mathematical concepts. [This paper will be published in "Journal of Mathematics Education."]