Final answer:
The missing step involves using geometric theorems to justify relationships between angles or segments in figures, employing concepts such as the Alternate Interior Angles Theorem and the properties of supplementary angles, as well as vector math principles like the dot product and cross product.
Step-by-step explanation:
The missing step in the given proof statements involves the application of geometric theorems to justify the equality or properties of angles or segments in figures. For example, the Alternate Interior Angles Theorem is used to establish that certain angles are equal because they are on the interior of two parallel lines cut by a transversal. Similarly, the knowledge that the sum of supplementary angles is 180 degrees can be used to prove the equality of certain angle pairs.
Geometric theorems such as the Law of Sines and the Law of Cosines are fundamental in solving problems related to triangles, providing relationships between angles and sides of a triangle. The dot product and cross product are concepts from vector mathematics, used to determine the relationship between vectors, such as whether they are perpendicular (orthogonal) or parallel.