Question

Complete the missing statements and reasons in the given proof involving angles and lines.

a) ZWZX and ZWZV are a linear pair. [Given]
b) m∠ZWZX + m∠ZWZV = 180 [Definition of Supplementary Angles]
c) ∠ZWZX = ∠ZWZV = 90 [Complementary angles are right angles. Definition of Perpendicular Lines]
d) WY || VX [Corresponding angles are congruent. Definition of Parallel Lines]

Answer 1

The proof involves identifying angle relationships and line parallels, starting with a linear pair of angles being defined as supplementary and thus right angles when equal, leading to establishing that the lines WY and VX are parallel due to the congruency of corresponding angles.

Step-by-step explanation:

The provided statements and reasons form a logical sequence of steps in a geometric proof dealing with angles and parallel lines. Here is the completion of the proof with explanations: ZWZX and ZWZV are a linear pair. [Given]. m∠ZWZX + m∠ZWZV = 180 [Definition of Supplementary Angles]. ∠ZWZX = ∠ZWZV = 90 [Since they are supplementary and equal, both are right angles; based on the definition of perpendicular lines which form right angles.]. WY || VX [Lines that form congruent and corresponding angles, as in right angles, are parallel. This is supported by the Definition of Parallel Lines]. The statements provided involve understanding the relationship between linear pairs, the definition of supplementary and perpendicular angles, and the characteristics of parallel lines and right angles, which are used to establish the parallel relationship between lines WY and VX.