Let's break down the questions step-by-step based on the given information about triangles ZWX and YXW being congruent.
Question 1
Which corresponding parts statement is needed to prove △ZWR≅△YXR? The necessary corresponding parts that we could use to prove triangles are congruent should include one of the pairs of sides or angles. Given that WX is a shared side in triangles ZWR and YXR, the statement needed is:
Response: WX = WX
Question 2
A classmate writes the statement ∠ZRW≅∠YRX to help prove the congruence of the triangles. What reason should the classmate give?
Since ∠ZRW and ∠YRX are opposite angles formed by the intersection of line segments WZ and XY, they are vertical angles. Therefore, the appropriate reason is:
Response: Vertical Angles Thm
Question 3
After using the congruence statements in the previous 2 problems, which statement can be used to prove the triangles congruent?
Given that we have established that WX is congruent to itself (reflexive), and that ∠ZRW is congruent to ∠YRX (by the Vertical Angles theorem), we can utilize the angle and side we have gathered to support our triangles’ congruency. However, we do not have the measure of angles Z and Y directly from the information provided, so the strongest choice here will still be:
Response: WR ≅ RX
Question 4
Which theorem or postulate will prove △ZWR≅△YXR?
We now have information on a pair of sides (WX) that are equal, the angles (∠ZRW ≅ ∠YRX) are equal, and we also have WR ≅ RX. Consequently, the best theorem that applies here with two sides and the angle between them is:
Response: SAS (Side-Angle-Side)
These answers should guide you through the congruency proofs for the triangles based on the information provided.