Question

directions: determine whether the triangles are similar. if similar, state how (a or sas), and write a similarity statement.
1
2
3
4
5
6
7
8

Explanation:

Step1: Analyze triangle similarity for problem 7

For \(\triangle XYZ\) and \(\triangle GHJ\), in \(\triangle XYZ\), \(\angle Z = 90^{\circ}\), \(\angle X=61^{\circ}\), so \(\angle Y=180^{\circ}-90^{\circ}-61^{\circ} = 29^{\circ}\). In \(\triangle GHJ\), \(\angle G = 90^{\circ}\), \(\angle J = 34^{\circ}\), so \(\angle H=180^{\circ}-90^{\circ}-34^{\circ}=56^{\circ}\). Since the corresponding angles are not equal, the triangles are not similar.

Step2: Analyze triangle similarity for problem 8

For \(\triangle QRS\) and \(\triangle TUS\), \(\frac{QR}{TR}=\frac{52}{63}\), \(\frac{RS}{US}=\frac{39}{84}=\frac{13}{28}\). Since \(\frac{52}{63}
eq\frac{13}{28}\), the triangles are not similar by the Side - Side - Side (SSS) similarity criterion (if the ratios of the corresponding sides are not equal, the triangles are not similar).

Answer:

1. Not similar.
2. Not similar.