Final answer:
The questions relate to geometry and algebra, discussing topics like congruent triangles, algebraic expressions, and the Pythagorean theorem.
Step-by-step explanation:
The questions posted above involve mathematical concepts related to congruence, equality, proportions, similar triangles, and the Pythagorean theorem; each addressing different aspects of geometry and algebra.
For example, the congruence statement question requires an understanding of how triangle congruence is expressed and depends on the correspondence of angles and sides. With congruent triangles, the order of vertices in the notation matters as it indicates which angles and sides of the two triangles are congruent to each other. In this case, the order of the vertices in the congruence statement should match the corresponding parts of each triangle that are conjectured or known to be congruent.
When it comes to expressions involving variables and multiplications, such as A × F = B × F, we cannot conclude A = B unless additional information (such as F ≠ 0) is provided. With expressions like FÃ = BF, we look for the presence of a scalar multiplier or other properties to establish equality.
The Pythagorean theorem, a² + b² = c², is a fundamental principle in mathematics that relates the lengths of the sides of a right triangle and is often used to solve for an unknown side.