Question

choose one option from each drop-down menu to answer the question.
in figures jklm and pqrs, the quotient of sides jk and pq is equivalent to
all of the other quotients
choose...
therefore, ✔ all of the other quotients ig side lengths
of the figures sh none of the other quotients
dilation of figure only the quotient of sides lm and rs
quotients are ec only the quotients of sides kl and qr and sides mj and sp

Explanation:

Step1: Recall Similar Figures Property

For similar figures (like J K L M and P Q R S, assuming they are similar, e.g., via dilation), the ratios of corresponding sides are equal. So the quotient of J K and P Q (a pair of corresponding sides) should equal the quotient of other corresponding side pairs (e.g., K L / Q R, L M / R S, M J / S P).

Step2: Evaluate the Options

• "none of the other quotients": Contradicts the similar figures side - ratio property.
• "only the quotient of sides L M and R S": Incorrect, as all corresponding side quotients should be equal, not just this one.
• "only the quotients of sides K L and Q R and sides M J and S P": Incorrect, as all corresponding side quotients (including J K / P Q, K L / Q R, L M / R S, M J / S P) are equal.
• "all of the other quotients": Correct, because in similar figures, the ratio of any pair of corresponding sides is the same (the scale factor), so the quotient of J K and P Q is equivalent to all other quotients of corresponding sides.

Answer:

all of the other quotients