What is the typical CCSS approach to solving a geometry problem involving similar triangles?

• A. Apply Pythagorean theorem.
• B. Use trigonometric functions to compute angles.
• C. Use similarity ratios and proportional reasoning.
• D. Use random experimentation with coordinates.

Answer: (C)

Similar triangles share a constant scale factor between their corresponding sides, so the usual CCSS approach is to use similarity ratios and proportional reasoning. Once you know triangles are similar, you set up a proportion using a pair of corresponding sides and solve for any unknown lengths. This works because every pair of corresponding sides grows or shrinks by the same factor, so once one side is known, all others follow by multiplying or cross-multiplying to form equations.

This method is preferred because it directly uses the defining property of similarity: the ratios of corresponding sides are equal. Pythagorean theorem applies to right triangles and isn’t the standard tool for establishing similarity itself. Trigonometric functions can help in some problems, but the common, straightforward strategy for similar triangles is to use proportional relationships. Relying on random coordinate experiments isn’t systematic or reliable for these problems.