Final answer:
The question requests the reasoning for each statement in a geometrical proof, touching upon concepts such as congruent angles, side congruency, trigonometry, logical deduction, and the Pythagorean Theorem.
Step-by-step explanation:
The student's question revolves around providing reasons for each statement in a geometrical proof. In geometry, reasons in a proof are based on definitions, properties, postulates, and previously proven theorems. For example, if it is given that °<1 is congruent to °<2, this could be justified by the definition of congruent angles or a specific theorem stating the conditions under which two angles are congruent.
When working with congruencies, such as WX is congruent to ZY, we typically use the notion of side-side-side (SSS) congruence postulate or other congruence theorems depending on the additional information provided in the problem. The use of trigonometry to determine the magnitude of weight components or force vectors in physics showcases mathematical applications in real-world scenarios, which is consistent with the principles of deductive reasoning and mathematical logic. The Pythagorean Theorem and its reliability in mathematics is mentioned as an example of logical deduction from postulates, highlighting the systematic nature of mathematical proofs and the importance of the logical flow from premises to a conclusion. This is akin to a disjunctive syllogism, a form of valid deductive inference, which is a fundamental concept in both mathematics and philosophy.