Final answer:
Option 4) 10/5 = 2.5/5 is the correct choice for the proof, as simplifying both sides of the equation demonstrates that the ratio of the sides of the triangles is proportional, thereby concluding that ΔWXZ is similar to ΔXYZ.
Step-by-step explanation:
The question seems to be related to verifying whether two triangles are similar by comparing the ratios of corresponding sides. The options provided give different fractions and ask which one correctly completes a proof of similarity for triangles ΔWXZ and ΔXYZ. To prove that two triangles are similar, the corresponding sides must be in proportion, meaning the ratios must be equivalent.
From the information provided in the background examples, we're looking for proportions where the scales are set equal to each other (unit scale) to form equivalent ratios. For example:
- Length scale/actual in inches/feet: 1/20 = 0.5/5
- Width scale/actual in inches/feet: w/10 = 0.5/5
Based on this, we can use cross multiplication to find which option correctly shows the proportional relationship between the sides. Cross multiplication would prove that the ratios are equal, thereby showing the triangles are similar.
Option 4) 10/5 = 2.5/5 is the correct choice because both sides of the equation reduce to the number 2 when simplified, confirming the proportionality of the sides of the triangles.