A geometrical proof is a method of using logical deductions and mathematical concepts to provide evidence for the truth of a mathematical statement or theorem. It involves using previously accepted principles and definitions to arrive at a conclusion.
Geometrical proofs are important because they help us understand and verify mathematical concepts and statements. They also improve our problem solving skills and logical reasoning abilities.
To construct a geometrical proof, you must first clearly state the theorem or statement you are trying to prove. Then, use previously accepted principles, definitions, and theorems to logically deduce each step until you arrive at the desired conclusion.
Some common techniques used in geometrical proofs include using axioms, postulates, theorems, and definitions, as well as properties of geometric shapes such as angles, triangles, and circles. Other techniques include using algebraic equations, coordinate geometry, and transformations.
To check the validity of a geometrical proof, one can carefully follow each step and make sure it is logically sound and follows the accepted principles and definitions. Additionally, one can use counterexamples or try to prove the statement using a different method to ensure it is true.