Question

Given that ∠wvy≅∠u, complete the proof that ∠w≅∠uxy.

Which of the following statements is a valid step in the proof?
A) ∠wvy ≅ ∠uxy (by Corresponding Angles Postulate)
B) ∠wvy ≅ ∠u (given)
C) ∠w ≅ ∠uxy (by Angle Addition Postulate)
D) ∠w ≅ ∠u (by Vertical Angles Theorem)

Answer 1

Option B) √ wvy ≅ √ u is the valid step in the proof, as it is provided in the given information and immediately applicable to the proof.

Step-by-step explanation:

Direct answer to the student's question is option B) √ wvy ≅ √ u. This is a given fact in the problem statement and hence a valid step in the proof that √ w ≅ √ uxy. To further explain, the reason why option B is correct is because it is explicitly stated as part of the given information which we can use as a starting point for our proof. Options A, C, and D do not provide a logical step that directly relates to proving that √ w ≅ √ uxy based on the given information alone.

A proof often starts with a given statement and then applies a series of established postulates, theorems, and corollaries to arrive at a conclusion. Therefore, by knowing √ wvy ≅ √ u, we can explore other relationships in the figures to establish that √ w ≅ √ uxy.