Question

directions: determine whether the triangles are similar by side - side - side similarity. if yes, write a similarity statement.
7.
8.

Explanation:

7.

Step1: Calculate the ratios of corresponding sides

For \(\triangle NKR\) and \(\triangle SED\):

• \(\frac{NK}{SE}=\frac{9}{21}=\frac{3}{7}\)
• \(\frac{NR}{SD}=\frac{13.5}{31.5}=\frac{3}{7}\)
• \(\frac{KR}{ED}=\frac{20.25}{49}=\frac{3}{7}\)

Step2: Check the similarity condition

Since \(\frac{NK}{SE}=\frac{NR}{SD}=\frac{KR}{ED}=\frac{3}{7}\), by the Side - Side - Side (SSS) similarity criterion, \(\triangle NKR\sim\triangle SED\)

8.

Step1: Calculate the ratios of corresponding sides

For \(\triangle WXV\) and \(\triangle YXU\):

• \(\frac{WX}{YX}=\frac{15}{6}=\frac{5}{2}\)
• \(\frac{WV}{YU}=\frac{20}{42}=\frac{10}{21}\)
• \(\frac{XV}{XU}=\frac{30}{8}=\frac{15}{4}\)

Step2: Check the similarity condition

Since \(\frac{WX}{YX}
eq\frac{WV}{YU}
eq\frac{XV}{XU}\), \(\triangle WXV\) and \(\triangle YXU\) are not similar by the SSS similarity criterion

Answer:

1. \(\triangle NKR\sim\triangle SED\)
2. The triangles are not similar by SSS similarity.