Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the relationship between the sides of similar triangles?

They are always equal in length
They are not proportional
Corresponding sides are proportional
They can have different angles

The correct answer is: Corresponding sides are proportional

The correct answer highlights that in similar triangles, corresponding sides maintain a proportional relationship. This means that the ratios of the lengths of the corresponding sides of similar triangles are equal. For instance, if one triangle has sides of lengths 3, 4, and 5, and a similar triangle has sides of lengths 6, 8, and 10, the sides can be compared as follows: 3/6 = 1/2, 4/8 = 1/2, and 5/10 = 1/2. This proportionality is a fundamental property of similar triangles and is essential in solving various geometric problems. Regarding the other options, the idea that the sides are always equal in length is misleading. Similar triangles can be different sizes, but their corresponding sides will always have the same ratio. The statement about the sides being not proportional misrepresents the nature of similar triangles, as their defining feature is indeed this proportionality. Lastly, while it is true that similar triangles can have different angles, the essence of the question focuses on the relationship of their sides, making proportionality the key concept to understand.