Question

determine if triangle cde and triangle fgh are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.) answer attempt 1 out of 2

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(CDE\) with sides \(20\), \(27\), \(31\) and triangle \(FGH\) with sides \(100\), \(135\), \(155\).

• Ratio of first pair: \(\frac{100}{20}=5\)
• Ratio of second pair: \(\frac{135}{27} = 5\)
• Ratio of third pair: \(\frac{155}{31}=5\)

Step2: Check the Side - Side - Side (SSS) similarity criterion

Since \(\frac{FG}{CD}=\frac{FH}{CE}=\frac{GH}{DE} = 5\) (by SSS similarity criterion: if the ratios of the corresponding sides of two triangles are equal, then the triangles are similar)

Answer:

Triangle \(CDE\) and triangle \(FGH\) are similar by the Side - Side - Side (SSS) similarity criterion.