Question

Which of the following best completes the proof showing that ��wxz ��xyz?

1) 5 over 10 equals 5 over 2 and one half
2) 5 over 10 equals 5 over 5
3) 10 over 5 equals 5 over 2 and one half
4) 10 over 5 equals 2 and one half over 5

Answer 1

The correct completion of the proof is option 1, which correctly identifies '5 over 10 equals 5 over 2 and one half' as an instance of equivalent fractions, necessary for establishing angle equivalence in geometry.

Step-by-step explanation:

To determine which statement completes the proof that ∠wxz ≈ ∠xyz, we need to analyze the proportions given in the options to find equivalence in fractions. For instance, two fractions are equivalent if their cross multiplication yields the same product, which is a fundamental characteristic when finding a common denominator.

When assessing the statement '5 over 10 equals 5 over 2 and one half,' it's clear that both fractions reduce to 1/2, showing equivalence. This concept of equivalent fractions is crucial in identifying equal angles in a geometric proof based on proportional reasoning, as seen in the requirement to show that ∠wxz ≈ ∠xyz. Therefore, it seems the second option '5 over 10 equals 5 over 5' is incorrect, as 5/10 simplifies to 1/2, while 5/5 simplifies to 1, indicating these fractions are not equivalent.

Option 4 suggests '10 over 5 equals 2 and one half over 5,' which, when the fractions are simplified, results in 2 equals 1/2, clearly incorrect. Thus, based on the basic principles of finding a common denominator and equivalent fractions, option 1 is correct within the context of this mathematical proof.