nÃo hà / Neste trabalho apresentamos algumas relaÃÃes trigonomÃtricas fundamentais e suas demonstraÃÃes. Tais relaÃÃes merecem destaque, pois sÃo essenciais na resoluÃÃo de problemas nas diversas Ãreas do conhecimento. Inicialmente fizemos um breve histÃrico da Trigonometria destacando a sua importÃncia no contexto da MatemÃtica. Em sequÃncia apresentamos as relaÃÃes fundamentais, dentre elas, enfatizamos as fÃrmulas da adiÃÃo de arcos, cujas demonstraÃÃes utilizamos Ãrea de figuras planas, a lei dos cossenos e a lei dos senos. AlÃm disso, mostramos como estas fÃrmulas se relacionam com o Teorema da Corda Quebrada e o Teorema de Ptolomeu da Geometria Plana. Explorando a relaÃÃes entre Trigonometria e Geometria Plana. Procuramos mostrar a importÃncia desta teoria no ensino mÃdio motivando alunos e professores a buscar um maior interesse pelo conhecimento em MatemÃtica. / The present research aims to present classic demonstrations of the fundamental relations of Trigonometry,with a simple approach, and exploring flat shapes. The intention is to make such demonstrations better known and provide a highlight for Trigonometry, since they are essential in solving problems of everyday life. For this purpose, we made a historical highlighting of the importance of trigonometry in the mathematical context. Since we know Trigonometry is loosing its status and not being considered essential in basic education anymore, such demonstrations, associated with the flat shapes, may be used as a model class. Therefore, we highlight the following fundamental relations: Basic Trigonometric relations, Derived Relations, Sine of the Sum and Difference of Two Arcs, Cosine of the Sum and Difference of Two Arcs, Double Arcs, Half Arc, Transformation in Product and Applications. For the demonstration ot these relations we used some area results, cosine law, Ptolemyâs theorem and the theorem of the broken chord Plane Geometry. We believe that Trigonometry is linked to the formation of these flat shapes. Thus, such demonstrationas associated to these flat shapes may serve to improve the Trigonometry teaching- learning and as motivator for students and teachers seeking to enhance their knowledge in mathematics.