Question

use deductive reasoning to complete the following sentence. squares have equal diagonals. some rhombuses are squares. therefore,... some squares are rhombuses. some rhombuses have equal diagonals. some rhombuses do not have equal diagonals. rhombuses have equal sides.

Explanation:

We know two facts: 1. Squares have equal diagonals. 2. Some rhombuses are squares. By deductive reasoning, if some rhombuses are squares (and squares have equal diagonals), then those rhombuses that are squares must have equal diagonals. So we can conclude that some rhombuses have equal diagonals.

• Option "some squares are rhombuses" is a restatement of "some rhombuses are squares" (just reversed) and not the conclusion from the given premises about diagonals.
• Option "some rhombuses do not have equal diagonals" can't be concluded from the given information as we only know about the rhombuses that are squares (which have equal diagonals), we don't have info about other rhombuses.
• Option "rhombuses have equal sides" is a general property of rhombuses but it's not related to the given premises about squares and their diagonals, so it's not the conclusion from the given deductive reasoning setup.

Answer:

some rhombuses have equal diagonals.