With similar triangles, the ratios of all three pairs of corresponding sides are never equal.A.TrueB.False

Break Down the Problem

1. Identify the concept of similar triangles.
2. Understand the properties of similar triangles, particularly regarding the ratios of corresponding sides.

Relevant Concepts

• Similar triangles have sides that are proportional.
• If triangle $\triangle ABC$ is similar to triangle $\triangle DEF$, then the following holds true: $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$

Analysis and Detail

• The statement claims that "the ratios of all three pairs of corresponding sides are never equal." To determine the truth of this statement, we have to consider the definition of similar triangles.
• By definition, if two triangles are similar, their corresponding sides' ratios are equal. Therefore, it is impossible for the ratios to "never" be equal if the triangles are indeed similar.

Verify and Summarize

• Since the definition states that the ratios of corresponding sides for similar triangles must be equal, the statement provided in the question is incorrect.

Final Answer

The answer is B. False. The ratios of all three pairs of corresponding sides of similar triangles are always equal.