Question

question 2 (5 points)
explain how you can determine that each pair of triangles is similar.

a angle - angle similarity theorem
b side - side - side similarity theorem
c side - angle - side similarity theorem

Explanation:

Step1: Calculate the ratios of corresponding sides

For the two triangles, calculate the ratios of the corresponding sides:

• For the sides \(4\) cm and \(12\) cm: \(\frac{4}{12}=\frac{1}{3}\)
• For the sides \(7\) cm and \(21\) cm: \(\frac{7}{21}=\frac{1}{3}\)
• For the sides \(4\) cm and \(12\) cm (another pair of equal - length sides in the isosceles triangles): \(\frac{4}{12}=\frac{1}{3}\)

Step2: Apply the Side - Side - Side (SSS) Similarity Theorem

Since \(\frac{4}{12}=\frac{7}{21}=\frac{4}{12}=\frac{1}{3}\), by the Side - Side - Side (SSS) Similarity Theorem, if the ratios of the corresponding sides of two triangles are equal, then the two triangles are similar.

Answer:

B. Side - Side - Side Similarity Theorem